Atkin-Lehner |
2+ 3- 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112k |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
3177833472 = 210 · 38 · 11 · 43 |
Discriminant |
Eigenvalues |
2+ 3- -4 4 11+ 4 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-12747,553930] |
[a1,a2,a3,a4,a6] |
Generators |
[57:112:1] |
Generators of the group modulo torsion |
j |
306845800996/4257 |
j-invariant |
L |
5.6953768136866 |
L(r)(E,1)/r! |
Ω |
1.2938543102484 |
Real period |
R |
2.2009343592837 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999982803 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34056k1 22704q1 |
Quadratic twists by: -4 -3 |