Atkin-Lehner |
2+ 31+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
85312a |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
359424 |
Modular degree for the optimal curve |
Δ |
5292939454447616 = 231 · 31 · 433 |
Discriminant |
Eigenvalues |
2+ 0 -1 0 3 1 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-200108,34276144] |
[a1,a2,a3,a4,a6] |
Generators |
[3300:187912:1] |
Generators of the group modulo torsion |
j |
3380470452981441/20190961664 |
j-invariant |
L |
6.4000451556634 |
L(r)(E,1)/r! |
Ω |
0.43211825764223 |
Real period |
R |
7.40543247698 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999962248 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85312w1 2666c1 |
Quadratic twists by: -4 8 |