Atkin-Lehner |
2- 3+ 23+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
78384q |
Isogeny class |
Conductor |
78384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
19972554227712 = 224 · 36 · 23 · 71 |
Discriminant |
Eigenvalues |
2- 3+ -4 4 4 -6 -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9760,-299264] |
[a1,a2,a3,a4,a6] |
Generators |
[114:238:1] |
Generators of the group modulo torsion |
j |
25104854795041/4876111872 |
j-invariant |
L |
4.3156343832713 |
L(r)(E,1)/r! |
Ω |
0.48681645425399 |
Real period |
R |
4.4325066939107 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999974465 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9798k1 |
Quadratic twists by: -4 |