Atkin-Lehner |
2+ 3+ 5+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
87360r |
Isogeny class |
Conductor |
87360 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
2119680 |
Modular degree for the optimal curve |
Δ |
124606738733568000 = 212 · 3 · 53 · 75 · 136 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7- -2 13- -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8397641,-9363831159] |
[a1,a2,a3,a4,a6] |
Generators |
[4413:198744:1] |
Generators of the group modulo torsion |
j |
15989531155800771865024/30421567073625 |
j-invariant |
L |
5.1056078606863 |
L(r)(E,1)/r! |
Ω |
0.088687063195334 |
Real period |
R |
1.9189600209497 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002483 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
87360cd1 43680ck1 |
Quadratic twists by: -4 8 |