Atkin-Lehner |
2- 3- 11+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
128832bi |
Isogeny class |
Conductor |
128832 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
1022976 |
Modular degree for the optimal curve |
Δ |
-13694898360287232 = -1 · 236 · 33 · 112 · 61 |
Discriminant |
Eigenvalues |
2- 3- 0 4 11+ -2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-117953,-16617153] |
[a1,a2,a3,a4,a6] |
Generators |
[69474815249:-3739926626304:23639903] |
Generators of the group modulo torsion |
j |
-692332063944625/52241891328 |
j-invariant |
L |
10.342096861949 |
L(r)(E,1)/r! |
Ω |
0.12825179393758 |
Real period |
R |
13.439833877349 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000030933 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128832f1 32208l1 |
Quadratic twists by: -4 8 |