Atkin-Lehner |
2+ 7+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
128576l |
Isogeny class |
Conductor |
128576 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
109824 |
Modular degree for the optimal curve |
Δ |
-3225714688 = -1 · 215 · 74 · 41 |
Discriminant |
Eigenvalues |
2+ -2 -2 7+ 0 -3 -4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4769,125215] |
[a1,a2,a3,a4,a6] |
Generators |
[23:168:1] [39:-8:1] |
Generators of the group modulo torsion |
j |
-152494664/41 |
j-invariant |
L |
7.1249858867163 |
L(r)(E,1)/r! |
Ω |
1.3832993765232 |
Real period |
R |
0.42922655285127 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000015944 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128576j1 64288l1 128576w1 |
Quadratic twists by: -4 8 -7 |