Atkin-Lehner |
2+ 13- 89- |
Signs for the Atkin-Lehner involutions |
Class |
120328f |
Isogeny class |
Conductor |
120328 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
653952 |
Modular degree for the optimal curve |
Δ |
241612913714432 = 28 · 139 · 89 |
Discriminant |
Eigenvalues |
2+ -2 -2 3 6 13- 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-90809,10475947] |
[a1,a2,a3,a4,a6] |
Generators |
[-113:4394:1] |
Generators of the group modulo torsion |
j |
30505984/89 |
j-invariant |
L |
5.1396216077076 |
L(r)(E,1)/r! |
Ω |
0.55785591454222 |
Real period |
R |
1.1516462952248 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000057774 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120328l1 |
Quadratic twists by: 13 |