Atkin-Lehner |
2- 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696eo |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
1571086281904128 = 212 · 39 · 117 |
Discriminant |
Eigenvalues |
2- 3+ 2 -4 11- 4 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-39204,-2299968] |
[a1,a2,a3,a4,a6] |
Generators |
[906:26568:1] |
Generators of the group modulo torsion |
j |
46656/11 |
j-invariant |
L |
5.8458699067933 |
L(r)(E,1)/r! |
Ω |
0.34507321594541 |
Real period |
R |
4.2352388099038 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001834 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696en1 34848bn1 69696es1 6336bk1 |
Quadratic twists by: -4 8 -3 -11 |