Atkin-Lehner |
2- 3- 13- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
69264x |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
12257639898192 = 24 · 316 · 13 · 372 |
Discriminant |
Eigenvalues |
2- 3- 0 -2 0 13- -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-54120,4843087] |
[a1,a2,a3,a4,a6] |
j |
1502967414784000/1050895053 |
j-invariant |
L |
1.412159636614 |
L(r)(E,1)/r! |
Ω |
0.70607981822029 |
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 |
17316c1 23088s1 |
Quadratic twists by: -4 -3 |