Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192t |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
-320907130990704 = -1 · 24 · 36 · 317 |
Discriminant |
Eigenvalues |
2+ 3- 3 -3 2 4 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,8649,-804357] |
[a1,a2,a3,a4,a6] |
Generators |
[5487:406503:1] |
Generators of the group modulo torsion |
j |
6912/31 |
j-invariant |
L |
8.2039240593664 |
L(r)(E,1)/r! |
Ω |
0.27411206944809 |
Real period |
R |
3.7411359138497 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998918 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7688h1 2232g1 |
Quadratic twists by: -3 -31 |