Atkin-Lehner |
2+ 3- 83- |
Signs for the Atkin-Lehner involutions |
Class |
47808x |
Isogeny class |
Conductor |
47808 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
313668288 = 26 · 310 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 2 4 4 -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-80679,8820412] |
[a1,a2,a3,a4,a6] |
Generators |
[21463956:3682822220:729] |
Generators of the group modulo torsion |
j |
1244794697213248/6723 |
j-invariant |
L |
8.586557394392 |
L(r)(E,1)/r! |
Ω |
1.1696990832143 |
Real period |
R |
14.681651918207 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999913 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47808m1 23904r4 15936j1 |
Quadratic twists by: -4 8 -3 |