Atkin-Lehner |
2+ 3- 17+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
31008f |
Isogeny class |
Conductor |
31008 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
101376 |
Modular degree for the optimal curve |
Δ |
133134574091328 = 26 · 32 · 173 · 196 |
Discriminant |
Eigenvalues |
2+ 3- 2 2 -2 -2 17+ 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-61242,-5827392] |
[a1,a2,a3,a4,a6] |
Generators |
[1749:72390:1] |
Generators of the group modulo torsion |
j |
396916291562341312/2080227720177 |
j-invariant |
L |
8.2739631745691 |
L(r)(E,1)/r! |
Ω |
0.30358034160764 |
Real period |
R |
4.5424346488497 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31008l1 62016b2 93024bi1 |
Quadratic twists by: -4 8 -3 |