Atkin-Lehner |
2- 3- 5+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
85680dk |
Isogeny class |
Conductor |
85680 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
2949120 |
Modular degree for the optimal curve |
Δ |
480993898848583680 = 228 · 311 · 5 · 7 · 172 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ 0 -6 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7386123,7726251962] |
[a1,a2,a3,a4,a6] |
Generators |
[1279:19278:1] |
Generators of the group modulo torsion |
j |
14924020698027934921/161083883520 |
j-invariant |
L |
4.3282197987378 |
L(r)(E,1)/r! |
Ω |
0.26737271547587 |
Real period |
R |
2.0234954564018 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999983548 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10710bb1 28560cu1 |
Quadratic twists by: -4 -3 |