def two_descent(self,
verbose=True,
selmer_only=False,
first_limit=20,
second_limit=8,
n_aux=-1,
second_descent=True):
"""
Compute 2-descent data for this curve.
INPUT:
- ``verbose`` (bool, default ``True``) -- print what mwrank is doing.
- ``selmer_only`` (bool, default ``False``) -- ``selmer_only`` switch.
- ``first_limit`` (int, default 20) -- bound on `|x|+|z|` in
quartic point search.
- ``second_limit`` (int, default 8) -- bound on
`\log \max(|x|,|z|)`, i.e. logarithmic.
- ``n_aux`` (int, default -1) -- (only relevant for general
2-descent when 2-torsion trivial) number of primes used for
quartic search. ``n_aux=-1`` causes default (8) to be used.
Increase for curves of higher rank.
- ``second_descent`` (bool, default ``True``) -- (only relevant
for curves with 2-torsion, where mwrank uses descent via
2-isogeny) flag determining whether or not to do second
descent. *Default strongly recommended.*
OUTPUT:
Nothing -- nothing is returned.
TESTS (see #7992)::
sage: EllipticCurve([0, prod(prime_range(10))]).mwrank_curve().two_descent()
Basic pair: I=0, J=-5670
disc=-32148900
2-adic index bound = 2
2-adic index = 2
Two (I,J) pairs
Looking for quartics with I = 0, J = -5670
Looking for Type 3 quartics:
Trying positive a from 1 up to 5 (square a first...)
Trying positive a from 1 up to 5 (...then non-square a)
(2,0,-12,19,-6) --nontrivial...(x:y:z) = (2 : 4 : 1)
Point = [-2488:-4997:512]
height = 6.46767239...
Rank of B=im(eps) increases to 1
Trying negative a from -1 down to -3
Finished looking for Type 3 quartics.
Looking for quartics with I = 0, J = -362880
Looking for Type 3 quartics:
Trying positive a from 1 up to 20 (square a first...)
Trying positive a from 1 up to 20 (...then non-square a)
Trying negative a from -1 down to -13
Finished looking for Type 3 quartics.
Mordell rank contribution from B=im(eps) = 1
Selmer rank contribution from B=im(eps) = 1
Sha rank contribution from B=im(eps) = 0
Mordell rank contribution from A=ker(eps) = 0
Selmer rank contribution from A=ker(eps) = 0
Sha rank contribution from A=ker(eps) = 0
sage: EllipticCurve([0, prod(prime_range(100))]).mwrank_curve().two_descent()
Traceback (most recent call last):
...
RuntimeError: Aborted
"""
from sage.libs.mwrank.mwrank import _two_descent # import here to save time
first_limit = int(first_limit)
second_limit = int(second_limit)
n_aux = int(n_aux)
second_descent = int(
second_descent) # convert from bool to (int) 0 or 1
# TODO: Don't allow limits above some value...???
# (since otherwise mwrank just sets limit tiny)
self.__descent = _two_descent()
self.__descent.do_descent(self.__curve, verbose, selmer_only,
first_limit, second_limit, n_aux,
second_descent)
if not self.__two_descent_data().ok():
raise RuntimeError, "A 2-descent did not complete successfully."
def two_descent(self,
verbose = True,
selmer_only = False,
first_limit = 20,
second_limit = 8,
n_aux = -1,
second_descent = True):
"""
Compute 2-descent data for this curve.
INPUT:
- ``verbose`` (bool, default ``True``) -- print what mwrank is doing.
- ``selmer_only`` (bool, default ``False``) -- ``selmer_only`` switch.
- ``first_limit`` (int, default 20) -- bound on `|x|+|z|` in
quartic point search.
- ``second_limit`` (int, default 8) -- bound on
`\log \max(|x|,|z|)`, i.e. logarithmic.
- ``n_aux`` (int, default -1) -- (only relevant for general
2-descent when 2-torsion trivial) number of primes used for
quartic search. ``n_aux=-1`` causes default (8) to be used.
Increase for curves of higher rank.
- ``second_descent`` (bool, default ``True``) -- (only relevant
for curves with 2-torsion, where mwrank uses descent via
2-isogeny) flag determining whether or not to do second
descent. *Default strongly recommended.*
OUTPUT:
Nothing -- nothing is returned.
TESTS (see #7992)::
sage: EllipticCurve([0, prod(prime_range(10))]).mwrank_curve().two_descent()
sage: EllipticCurve([0, prod(prime_range(100))]).mwrank_curve().two_descent()
Traceback (most recent call last):
...
RuntimeError: Aborted
"""
from sage.libs.mwrank.mwrank import _two_descent # import here to save time
first_limit = int(first_limit)
second_limit = int(second_limit)
n_aux = int(n_aux)
second_descent = int(second_descent) # convert from bool to (int) 0 or 1
# TODO: Don't allow limits above some value...???
# (since otherwise mwrank just sets limit tiny)
self.__descent = _two_descent()
self.__descent.do_descent(self.__curve,
verbose,
selmer_only,
first_limit,
second_limit,
n_aux,
second_descent)
if not self.__two_descent_data().ok():
raise RuntimeError, "A 2-descent did not complete successfully."
def two_descent(
self, verbose=True, selmer_only=False, first_limit=20, second_limit=8, n_aux=-1, second_descent=True
):
"""
Compute 2-descent data for this curve.
INPUT:
- ``verbose`` (bool, default ``True``) -- print what mwrank is doing.
- ``selmer_only`` (bool, default ``False``) -- ``selmer_only`` switch.
- ``first_limit`` (int, default 20) -- bound on `|x|+|z|` in
quartic point search.
- ``second_limit`` (int, default 8) -- bound on
`\log \max(|x|,|z|)`, i.e. logarithmic.
- ``n_aux`` (int, default -1) -- (only relevant for general
2-descent when 2-torsion trivial) number of primes used for
quartic search. ``n_aux=-1`` causes default (8) to be used.
Increase for curves of higher rank.
- ``second_descent`` (bool, default ``True``) -- (only relevant
for curves with 2-torsion, where mwrank uses descent via
2-isogeny) flag determining whether or not to do second
descent. *Default strongly recommended.*
OUTPUT:
Nothing -- nothing is returned.
TESTS (see #7992)::
sage: EllipticCurve([0, prod(prime_range(10))]).mwrank_curve().two_descent()
Basic pair: I=0, J=-5670
disc=-32148900
2-adic index bound = 2
2-adic index = 2
Two (I,J) pairs
Looking for quartics with I = 0, J = -5670
Looking for Type 3 quartics:
Trying positive a from 1 up to 5 (square a first...)
Trying positive a from 1 up to 5 (...then non-square a)
(2,0,-12,19,-6) --nontrivial...(x:y:z) = (2 : 4 : 1)
Point = [-2488:-4997:512]
height = 6.46767239...
Rank of B=im(eps) increases to 1
Trying negative a from -1 down to -3
Finished looking for Type 3 quartics.
Looking for quartics with I = 0, J = -362880
Looking for Type 3 quartics:
Trying positive a from 1 up to 20 (square a first...)
Trying positive a from 1 up to 20 (...then non-square a)
Trying negative a from -1 down to -13
Finished looking for Type 3 quartics.
Mordell rank contribution from B=im(eps) = 1
Selmer rank contribution from B=im(eps) = 1
Sha rank contribution from B=im(eps) = 0
Mordell rank contribution from A=ker(eps) = 0
Selmer rank contribution from A=ker(eps) = 0
Sha rank contribution from A=ker(eps) = 0
sage: EllipticCurve([0, prod(prime_range(100))]).mwrank_curve().two_descent()
Traceback (most recent call last):
...
RuntimeError: Aborted
"""
from sage.libs.mwrank.mwrank import _two_descent # import here to save time
first_limit = int(first_limit)
second_limit = int(second_limit)
n_aux = int(n_aux)
second_descent = int(second_descent) # convert from bool to (int) 0 or 1
# TODO: Don't allow limits above some value...???
# (since otherwise mwrank just sets limit tiny)
self.__descent = _two_descent()
self.__descent.do_descent(self.__curve, verbose, selmer_only, first_limit, second_limit, n_aux, second_descent)
if not self.__two_descent_data().ok():
raise RuntimeError("A 2-descent did not complete successfully.")