Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192k |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1474560 |
Modular degree for the optimal curve |
Δ |
-2.4979731983447E+19 |
Discriminant |
Eigenvalues |
2+ 3- -1 -3 -2 -4 -4 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1213743,568084579] |
[a1,a2,a3,a4,a6] |
Generators |
[527:-8649:1] |
Generators of the group modulo torsion |
j |
-19102326016/2413071 |
j-invariant |
L |
3.0197382703252 |
L(r)(E,1)/r! |
Ω |
0.20603755700543 |
Real period |
R |
1.8320314473081 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000799 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23064l1 2232f1 |
Quadratic twists by: -3 -31 |