Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
8712h |
Isogeny class |
Conductor |
8712 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
42240 |
Modular degree for the optimal curve |
Δ |
-9721096369281792 = -1 · 28 · 311 · 118 |
Discriminant |
Eigenvalues |
2+ 3- 0 -1 11- 6 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-79860,9897316] |
[a1,a2,a3,a4,a6] |
Generators |
[242:-2178:1] |
Generators of the group modulo torsion |
j |
-1408000/243 |
j-invariant |
L |
4.3243102411427 |
L(r)(E,1)/r! |
Ω |
0.39318866569522 |
Real period |
R |
0.45825225674388 |
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 |
17424o1 69696bj1 2904m1 8712v1 |
Quadratic twists by: -4 8 -3 -11 |