Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696co |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
81920 |
Modular degree for the optimal curve |
Δ |
247961850048 = 26 · 37 · 116 |
Discriminant |
Eigenvalues |
2+ 3- 2 -4 11- -2 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4719,122452] |
[a1,a2,a3,a4,a6] |
Generators |
[176:2178:1] |
Generators of the group modulo torsion |
j |
140608/3 |
j-invariant |
L |
5.5326072636063 |
L(r)(E,1)/r! |
Ω |
0.98579285876821 |
Real period |
R |
1.4030856517027 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001539 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696cl1 34848cg3 23232ch1 576b1 |
Quadratic twists by: -4 8 -3 -11 |