Atkin-Lehner |
2- 7- 17- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
61642x |
Isogeny class |
Conductor |
61642 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
306432 |
Modular degree for the optimal curve |
Δ |
19162172170624 = 27 · 77 · 173 · 37 |
Discriminant |
Eigenvalues |
2- -1 -3 7- 2 -2 17- -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-75412,7936725] |
[a1,a2,a3,a4,a6] |
Generators |
[-315:905:1] [-43:-3311:1] |
Generators of the group modulo torsion |
j |
403141222589617/162875776 |
j-invariant |
L |
10.583473822948 |
L(r)(E,1)/r! |
Ω |
0.67502895408636 |
Real period |
R |
0.18664938033397 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999814 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8806e1 |
Quadratic twists by: -7 |