Atkin-Lehner |
2+ 5+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
61600c |
Isogeny class |
Conductor |
61600 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
3705625000000 = 26 · 510 · 72 · 112 |
Discriminant |
Eigenvalues |
2+ 0 5+ 7+ 11+ -6 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3925,-19500] |
[a1,a2,a3,a4,a6] |
Generators |
[-16:198:1] |
Generators of the group modulo torsion |
j |
6687175104/3705625 |
j-invariant |
L |
3.8749238693107 |
L(r)(E,1)/r! |
Ω |
0.64625139388737 |
Real period |
R |
2.9980003957595 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000108 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
61600bp1 123200o2 12320j1 |
Quadratic twists by: -4 8 5 |