Atkin-Lehner |
2+ 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
8112c |
Isogeny class |
Conductor |
8112 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
19968 |
Modular degree for the optimal curve |
Δ |
-67659968922624 = -1 · 210 · 34 · 138 |
Discriminant |
Eigenvalues |
2+ 3+ 3 0 0 13+ -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,8056,-284064] |
[a1,a2,a3,a4,a6] |
Generators |
[110:1386:1] |
Generators of the group modulo torsion |
j |
69212/81 |
j-invariant |
L |
4.4397510570253 |
L(r)(E,1)/r! |
Ω |
0.33232904295971 |
Real period |
R |
3.3398759084407 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4056g1 32448de1 24336o1 8112d1 |
Quadratic twists by: -4 8 -3 13 |