Atkin-Lehner |
2+ 3- 11- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
70488c |
Isogeny class |
Conductor |
70488 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
709113511535616 = 210 · 312 · 114 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 2 2 11- -4 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-191739,32290310] |
[a1,a2,a3,a4,a6] |
Generators |
[3415:198000:1] |
Generators of the group modulo torsion |
j |
1044305586357988/949922721 |
j-invariant |
L |
8.4581138654083 |
L(r)(E,1)/r! |
Ω |
0.5051021146287 |
Real period |
R |
4.1863385739286 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000516 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23496c1 |
Quadratic twists by: -3 |