Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cn |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3686400 |
Modular degree for the optimal curve |
Δ |
4.3053788012653E+21 |
Discriminant |
Eigenvalues |
2+ 3- 2 -4 11- -2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5667519,4123528508] |
[a1,a2,a3,a4,a6] |
Generators |
[3013821992812:3231741241860140:52439613407] |
Generators of the group modulo torsion |
j |
243578556889408/52089208083 |
j-invariant |
L |
6.3367694873438 |
L(r)(E,1)/r! |
Ω |
0.13063850956045 |
Real period |
R |
24.253068670211 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001036 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696ck1 34848bb3 23232v1 6336n1 |
Quadratic twists by: -4 8 -3 -11 |