Test_2_Conjecture_5.sage

import os
import sys
import time
import sage.parallel.multiprocessing_sage
import itertools
from multiprocessing import Pool
from sage.databases.cremona import cremona_to_lmfdb, lmfdb_to_cremona
from sage.schemes.elliptic_curves.ell_modular_symbols import ModularSymbolECLIB

def TestConjectures(Ep):
	File = open('./Results.txt', 'a')
	Error = False
	E_Sage = EllipticCurve(Ep[0])
	E_Cremona = CremonaDatabase().data_from_coefficients(Ep[0])
	M_Cremona = ModularSymbolECLIB(E_Sage, +1)

	ord_period = E_Sage.j_invariant().denominator().valuation(Ep[1])
	torsion_period = Integer(E_Sage.tate_curve(Ep[1]).parameter().unit_part().expansion()[0])

	C_5 = 1
	if E_Cremona['rank'] == 0:
		Denominators = []
		for a in range(1, Ep[1]):
			Denominators.append(M_Cremona(Rational(a/Ep[1])))
		D = lcm(Denominators)

		LeftSide = 1
		RightSide = 1
		for a in range(1, Ep[1]):
			LeftSide = LeftSide * a**(D * ord_period * M_Cremona(Rational(a/Ep[1])) * E_Cremona['torsion_order'] * E_Cremona['torsion_order']) % Ep[1]

		RightSide = torsion_period^(2 * D * E_Cremona['db_extra'][0] * Integer(E_Cremona['db_extra'][-1]))

		if LeftSide % Ep[1] != RightSide % Ep[1] and LeftSide % Ep[1] != - RightSide % Ep[1]:
			C_5 = 0
			File.write(str(Ep) + ': ' + str(C_5))
				File.close()
				return None

	C_5 = -1
	File.write(str(Ep) + ': ' + str([C_5, C_5_L, C_6, C_6_L]))
    File.close()
    return None


if '__main__' == __name__:
	for i in ['00000-09999', '10000-19999', '20000-29999','30000-39999','40000-49999','50000-59999','60000-69999','70000-79999','80000-89999','90000-99999']:
		EllipticCurves = eval(open('./ModularSymbolsReady/{}.txt'.format(i), 'r').readlines()[0])
		E = eval(key)
		p = Integer(prime)
		TestConjectures([E,p])