Atkin-Lehner |
3+ 7- 19+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
86583d |
Isogeny class |
Conductor |
86583 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
294912 |
Modular degree for the optimal curve |
Δ |
758184189009177 = 3 · 712 · 19 · 312 |
Discriminant |
Eigenvalues |
1 3+ 0 7- -2 0 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-61520,-5747517] |
[a1,a2,a3,a4,a6] |
Generators |
[-158:323:1] [286:249:1] |
Generators of the group modulo torsion |
j |
218874659109625/6444459273 |
j-invariant |
L |
11.190119236017 |
L(r)(E,1)/r! |
Ω |
0.30368720846441 |
Real period |
R |
18.423757939206 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000049 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12369k1 |
Quadratic twists by: -7 |