Atkin-Lehner |
2- 3- 31+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69936w |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
2348640 |
Modular degree for the optimal curve |
Δ |
-9.3889348601762E+20 |
Discriminant |
Eigenvalues |
2- 3- -1 1 0 1 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-443061,1478449503] |
[a1,a2,a3,a4,a6] |
Generators |
[1971:90918:1] |
Generators of the group modulo torsion |
j |
-37572950224353624064/3667552679756315619 |
j-invariant |
L |
7.6412989838712 |
L(r)(E,1)/r! |
Ω |
0.12905060613055 |
Real period |
R |
5.9211647375659 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000007 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17484b1 |
Quadratic twists by: -4 |