def lpp_table(self):
"""generate the large putative primes table"""
output_str = r"${Delta_K}$ & $\Q(\sqrt{{{D}}})$ & {large_putative_primes}\\"
latex_output = []
for D in range(-self.range, self.range + 1):
if Integer(D).is_squarefree():
if not D in CLASS_NUMBER_ONE_DISCS:
if D != 1:
K = QuadraticField(D)
Delta_K = K.discriminant()
candidates = get_isogeny_primes(K,
aux_prime_count=25,
bound=2000,
loop_curves=False)
candidates = [
c for c in candidates
if c not in EC_Q_ISOGENY_PRIMES
]
candidates = [c for c in candidates if c > 71]
candidates.sort()
large_putative_primes = ", ".join(map(str, candidates))
output_here = output_str.format(
Delta_K=Delta_K,
D=D,
large_putative_primes=large_putative_primes,
)
latex_output.append(output_here)
for one_line in latex_output:
print(one_line)
def test_interval(self):
R = 100
for D in range(-R, R + 1):
if Integer(D).is_squarefree():
if not D in CLASS_NUMBER_ONE_DISCS:
if D != 1:
K = QuadraticField(D)
superset = get_isogeny_primes(K, AUX_PRIME_COUNT)
self.assertTrue(
set(superset).issuperset(EC_Q_ISOGENY_PRIMES))
def test_73_Box(self):
K = QuadraticField(-31)
superset = get_isogeny_primes(K, AUX_PRIME_COUNT)
self.assertTrue(set(superset).issuperset(EC_Q_ISOGENY_PRIMES))
self.assertIn(73, superset)
def test_311(self):
K = QuadraticField(11 * 17 * 9011 * 23629)
superset = get_isogeny_primes(K, AUX_PRIME_COUNT)
self.assertTrue(set(superset).issuperset(EC_Q_ISOGENY_PRIMES))
self.assertIn(311, superset)
def test_191(self):
K = QuadraticField(61 * 229 * 145757)
superset = get_isogeny_primes(K, AUX_PRIME_COUNT)
self.assertTrue(set(superset).issuperset(EC_Q_ISOGENY_PRIMES))
self.assertIn(191, superset)
def test_103(self):
K = QuadraticField(5 * 577)
superset = get_isogeny_primes(K, AUX_PRIME_COUNT)
self.assertTrue(set(superset).issuperset(EC_Q_ISOGENY_PRIMES))
self.assertIn(103, superset)
def test_73(self):
K = QuadraticField(-127)
superset = get_isogeny_primes(K, AUX_PRIME_COUNT, loop_curves=True)
self.assertTrue(set(superset).issuperset(EC_Q_ISOGENY_PRIMES))
self.assertIn(73, superset)