Atkin-Lehner |
2- 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696gi |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
-858991424631081984 = -1 · 210 · 316 · 117 |
Discriminant |
Eigenvalues |
2- 3- 2 2 11- 6 -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-336864,-87473320] |
[a1,a2,a3,a4,a6] |
j |
-3196715008/649539 |
j-invariant |
L |
3.5284768455848 |
L(r)(E,1)/r! |
Ω |
0.098013245927352 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696cj1 17424bx1 23232dd1 6336ch1 |
Quadratic twists by: -4 8 -3 -11 |