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)