Atkin-Lehner |
11- 17+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
121363f |
Isogeny class |
Conductor |
121363 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
243000 |
Modular degree for the optimal curve |
Δ |
-6185304252523 = -1 · 116 · 17 · 593 |
Discriminant |
Eigenvalues |
-2 0 -2 2 11- -4 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-4961,-180018] |
[a1,a2,a3,a4,a6] |
Generators |
[108:737:1] |
Generators of the group modulo torsion |
j |
-7622111232/3491443 |
j-invariant |
L |
1.9217068727684 |
L(r)(E,1)/r! |
Ω |
0.27828850739716 |
Real period |
R |
2.3018160976292 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999998669544 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1003d1 |
Quadratic twists by: -11 |