Atkin-Lehner |
2+ 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400bo |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
189851761406250000 = 24 · 311 · 510 · 193 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -3 2 6 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-159375,-12659375] |
[a1,a2,a3,a4,a6] |
j |
3930400000/1666737 |
j-invariant |
L |
0.9928138888427 |
L(r)(E,1)/r! |
Ω |
0.2482034743119 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34200cp1 22800z1 68400co1 |
Quadratic twists by: -4 -3 5 |