Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696bu |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
202752 |
Modular degree for the optimal curve |
Δ |
-90010151567424 = -1 · 26 · 38 · 118 |
Discriminant |
Eigenvalues |
2+ 3- -1 2 11- -1 -5 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-43923,3572404] |
[a1,a2,a3,a4,a6] |
Generators |
[-208:1926:1] |
Generators of the group modulo torsion |
j |
-937024/9 |
j-invariant |
L |
5.7402090929119 |
L(r)(E,1)/r! |
Ω |
0.60641314856706 |
Real period |
R |
4.7329193841721 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002739 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696bx1 34848n1 23232bq1 69696bw1 |
Quadratic twists by: -4 8 -3 -11 |