Atkin-Lehner |
2- 11- 71- |
Signs for the Atkin-Lehner involutions |
Class |
68728g |
Isogeny class |
Conductor |
68728 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
8640 |
Modular degree for the optimal curve |
Δ |
-16632176 = -1 · 24 · 114 · 71 |
Discriminant |
Eigenvalues |
2- -1 1 0 11- -4 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-40,233] |
[a1,a2,a3,a4,a6] |
Generators |
[4:-11:1] [169:2189:1] |
Generators of the group modulo torsion |
j |
-30976/71 |
j-invariant |
L |
9.174221138394 |
L(r)(E,1)/r! |
Ω |
1.948102583261 |
Real period |
R |
0.78488518496976 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999746 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68728c1 |
Quadratic twists by: -11 |