Atkin-Lehner |
3- 11- 19+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69597f |
Isogeny class |
Conductor |
69597 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
10100736 |
Modular degree for the optimal curve |
Δ |
-5.4765820844458E+24 |
Discriminant |
Eigenvalues |
-1 3- 2 0 11- -6 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-19026914,117042125816] |
[a1,a2,a3,a4,a6] |
Generators |
[-5922:151312:1] [-17346:3087371:8] |
Generators of the group modulo torsion |
j |
-1044963757444680616550617/7512458277703462435143 |
j-invariant |
L |
7.52075921562 |
L(r)(E,1)/r! |
Ω |
0.065497696192552 |
Real period |
R |
6.3791550040902 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23199c1 |
Quadratic twists by: -3 |