Atkin-Lehner |
2- 31- 43- |
Signs for the Atkin-Lehner involutions |
Class |
85312ba |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
140 |
Product of Tamagawa factors cp |
deg |
7992320 |
Modular degree for the optimal curve |
Δ |
5.3013205002721E+23 |
Discriminant |
Eigenvalues |
2- -2 -1 -2 3 -3 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-23355681,25688235871] |
[a1,a2,a3,a4,a6] |
Generators |
[-5177:88752:1] [-3097:261392:1] |
Generators of the group modulo torsion |
j |
10749577844685078038162/4044586563317939173 |
j-invariant |
L |
6.9410444468801 |
L(r)(E,1)/r! |
Ω |
0.084530528488426 |
Real period |
R |
0.58652051270115 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999996683 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85312c1 21328b1 |
Quadratic twists by: -4 8 |