Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cs |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
-16936128 = -1 · 26 · 37 · 112 |
Discriminant |
Eigenvalues |
2+ 3- -2 3 11- 6 -4 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-66,-286] |
[a1,a2,a3,a4,a6] |
Generators |
[25:117:1] |
Generators of the group modulo torsion |
j |
-5632/3 |
j-invariant |
L |
6.6302861339802 |
L(r)(E,1)/r! |
Ω |
0.81710793144272 |
Real period |
R |
2.0285833359903 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000391 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696cu1 34848cc1 23232o1 69696cv1 |
Quadratic twists by: -4 8 -3 -11 |