Atkin-Lehner |
2- 3- 5+ 7- 59- |
Signs for the Atkin-Lehner involutions |
Class |
37170bd |
Isogeny class |
Conductor |
37170 |
Conductor |
∏ cp |
384 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
192521563250688000 = 216 · 39 · 53 · 73 · 592 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- 2 -2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-171743,-17415993] |
[a1,a2,a3,a4,a6] |
Generators |
[-205:3126:1] |
Generators of the group modulo torsion |
j |
768477130627648681/264089935872000 |
j-invariant |
L |
8.8798966720636 |
L(r)(E,1)/r! |
Ω |
0.24108188471461 |
Real period |
R |
0.38368259720892 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12390f1 |
Quadratic twists by: -3 |