Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
81312n |
Isogeny class |
Conductor |
81312 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
6050065057344 = 26 · 32 · 72 · 118 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- 11- 2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-18674,-968856] |
[a1,a2,a3,a4,a6] |
Generators |
[5735:434148:1] |
Generators of the group modulo torsion |
j |
6352182208/53361 |
j-invariant |
L |
4.6750888006929 |
L(r)(E,1)/r! |
Ω |
0.40860939384936 |
Real period |
R |
5.7207309359337 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001024 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
81312bo1 7392j1 |
Quadratic twists by: -4 -11 |