Atkin-Lehner |
2- 3- 7- 11+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
123354bw |
Isogeny class |
Conductor |
123354 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
491520 |
Modular degree for the optimal curve |
Δ |
-64485144928512 = -1 · 28 · 37 · 76 · 11 · 89 |
Discriminant |
Eigenvalues |
2- 3- 0 7- 11+ -7 -1 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,8860,-217209] |
[a1,a2,a3,a4,a6] |
Generators |
[190:531:8] [29:237:1] |
Generators of the group modulo torsion |
j |
105522070106375/88456988928 |
j-invariant |
L |
17.816496797903 |
L(r)(E,1)/r! |
Ω |
0.34292804075792 |
Real period |
R |
0.27059395312072 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999996887 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
41118c1 |
Quadratic twists by: -3 |