Atkin-Lehner |
3+ 7+ 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
69531b |
Isogeny class |
Conductor |
69531 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
302400 |
Modular degree for the optimal curve |
Δ |
-15125287092531 = -1 · 3 · 78 · 11 · 433 |
Discriminant |
Eigenvalues |
2 3+ -2 7+ 11+ -6 5 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-6974,294335] |
[a1,a2,a3,a4,a6] |
Generators |
[362:2103:8] [1050:10187:8] |
Generators of the group modulo torsion |
j |
-6507999232/2623731 |
j-invariant |
L |
14.983277327786 |
L(r)(E,1)/r! |
Ω |
0.65708916837196 |
Real period |
R |
2.5336113759288 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999365 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69531m1 |
Quadratic twists by: -7 |