Atkin-Lehner |
2+ 3- 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112m |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
13750231256319888 = 24 · 312 · 11 · 435 |
Discriminant |
Eigenvalues |
2+ 3- 0 3 11- 0 2 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-63255,2380421] |
[a1,a2,a3,a4,a6] |
Generators |
[-2360260:32988213:12167] |
Generators of the group modulo torsion |
j |
2399721162016000/1178860704417 |
j-invariant |
L |
7.7901822674945 |
L(r)(E,1)/r! |
Ω |
0.35240621119318 |
Real period |
R |
11.052844727516 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000107 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34056g1 22704a1 |
Quadratic twists by: -4 -3 |