Atkin-Lehner |
2+ 3+ 11- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
11682a |
Isogeny class |
Conductor |
11682 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
12336192 = 26 · 33 · 112 · 59 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 11- -4 -4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-438,3636] |
[a1,a2,a3,a4,a6] |
Generators |
[-20:74:1] [4:42:1] |
Generators of the group modulo torsion |
j |
344619542331/456896 |
j-invariant |
L |
4.4131174221396 |
L(r)(E,1)/r! |
Ω |
2.2475925154985 |
Real period |
R |
0.98174321895724 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
93456u1 11682n1 128502bi1 |
Quadratic twists by: -4 -3 -11 |