Atkin-Lehner |
2- 3+ 5+ 13- 83- |
Signs for the Atkin-Lehner involutions |
Class |
32370v |
Isogeny class |
Conductor |
32370 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-1135134975000000 = -1 · 26 · 3 · 58 · 133 · 832 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -2 4 13- 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-138196,-19897771] |
[a1,a2,a3,a4,a6] |
j |
-291884025403196036929/1135134975000000 |
j-invariant |
L |
2.2280097652435 |
L(r)(E,1)/r! |
Ω |
0.12377832029148 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
97110be1 |
Quadratic twists by: -3 |