Atkin-Lehner |
3- 5+ 11+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
68475c |
Isogeny class |
Conductor |
68475 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
57344 |
Modular degree for the optimal curve |
Δ |
128390625 = 32 · 56 · 11 · 83 |
Discriminant |
Eigenvalues |
-1 3- 5+ 0 11+ 6 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-4288,-108433] |
[a1,a2,a3,a4,a6] |
j |
558051585337/8217 |
j-invariant |
L |
2.3599114499132 |
L(r)(E,1)/r! |
Ω |
0.58997786331142 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2739c1 |
Quadratic twists by: 5 |