Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cv |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
168960 |
Modular degree for the optimal curve |
Δ |
-30003383855808 = -1 · 26 · 37 · 118 |
Discriminant |
Eigenvalues |
2+ 3- -2 -3 11- -6 4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7986,380666] |
[a1,a2,a3,a4,a6] |
Generators |
[121:1089:1] |
Generators of the group modulo torsion |
j |
-5632/3 |
j-invariant |
L |
3.0206264693244 |
L(r)(E,1)/r! |
Ω |
0.61504064519719 |
Real period |
R |
0.40927193092712 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994115 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696ct1 34848w1 23232p1 69696cs1 |
Quadratic twists by: -4 8 -3 -11 |