Atkin-Lehner |
2- 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696eu |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
137928013774848 = 218 · 33 · 117 |
Discriminant |
Eigenvalues |
2- 3+ 4 -2 11- -2 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-13068,-106480] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:555:1] |
Generators of the group modulo torsion |
j |
19683/11 |
j-invariant |
L |
8.196842416707 |
L(r)(E,1)/r! |
Ω |
0.47953668895629 |
Real period |
R |
4.2733134951869 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999991343 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696r1 17424bi1 69696ew1 6336bn1 |
Quadratic twists by: -4 8 -3 -11 |