Atkin-Lehner |
3- 5+ 11- 83- |
Signs for the Atkin-Lehner involutions |
Class |
68475i |
Isogeny class |
Conductor |
68475 |
Conductor |
∏ cp |
360 |
Product of Tamagawa factors cp |
deg |
3225600 |
Modular degree for the optimal curve |
Δ |
-7.6466777014993E+20 |
Discriminant |
Eigenvalues |
-1 3- 5+ -1 11- -7 -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-388463,1333665042] |
[a1,a2,a3,a4,a6] |
Generators |
[-773:34624:1] [-7834:226667:8] |
Generators of the group modulo torsion |
j |
-414908885277195049/48938737289595417 |
j-invariant |
L |
7.5541027060065 |
L(r)(E,1)/r! |
Ω |
0.13100721340889 |
Real period |
R |
0.16017147515637 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999985 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2739e1 |
Quadratic twists by: 5 |