Atkin-Lehner |
2- 31+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
85312q |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
15168 |
Modular degree for the optimal curve |
Δ |
-42314752 = -1 · 210 · 312 · 43 |
Discriminant |
Eigenvalues |
2- 0 2 -2 4 -6 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,16,312] |
[a1,a2,a3,a4,a6] |
Generators |
[138:620:27] |
Generators of the group modulo torsion |
j |
442368/41323 |
j-invariant |
L |
6.2593772536773 |
L(r)(E,1)/r! |
Ω |
1.5570098239371 |
Real period |
R |
4.0201270111136 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006228 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85312h1 21328f1 |
Quadratic twists by: -4 8 |