Atkin-Lehner |
3+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
45123d |
Isogeny class |
Conductor |
45123 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1028160 |
Modular degree for the optimal curve |
Δ |
-80133164499061791 = -1 · 315 · 137 · 89 |
Discriminant |
Eigenvalues |
1 3+ -3 -1 3 13+ 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-9680154,-11596393089] |
[a1,a2,a3,a4,a6] |
j |
-20783106726980601457/16601685399 |
j-invariant |
L |
1.5406410538802 |
L(r)(E,1)/r! |
Ω |
0.042795584836068 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3471a1 |
Quadratic twists by: 13 |