Atkin-Lehner |
2+ 3+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
81312d |
Isogeny class |
Conductor |
81312 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
614400 |
Modular degree for the optimal curve |
Δ |
2668078690288704 = 26 · 34 · 74 · 118 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ 11- -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-391354,94330744] |
[a1,a2,a3,a4,a6] |
j |
58465284603328/23532201 |
j-invariant |
L |
0.89470743751295 |
L(r)(E,1)/r! |
Ω |
0.44735370438817 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
81312bv1 7392k1 |
Quadratic twists by: -4 -11 |