Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696ci |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
7680866267086848 = 214 · 37 · 118 |
Discriminant |
Eigenvalues |
2+ 3- 2 2 11- -2 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-53724,-2278672] |
[a1,a2,a3,a4,a6] |
Generators |
[-206:216:1] |
Generators of the group modulo torsion |
j |
810448/363 |
j-invariant |
L |
8.1683609698293 |
L(r)(E,1)/r! |
Ω |
0.32697151653181 |
Real period |
R |
3.1227341513443 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000372 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696gj2 4356f2 23232t2 6336ba2 |
Quadratic twists by: -4 8 -3 -11 |