Atkin-Lehner |
3- 13+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
12051c |
Isogeny class |
Conductor |
12051 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2688 |
Modular degree for the optimal curve |
Δ |
-711599499 = -1 · 312 · 13 · 103 |
Discriminant |
Eigenvalues |
0 3- -1 2 0 13+ 3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,222,162] |
[a1,a2,a3,a4,a6] |
Generators |
[8:49:1] |
Generators of the group modulo torsion |
j |
1659797504/976131 |
j-invariant |
L |
3.6906869590117 |
L(r)(E,1)/r! |
Ω |
0.97564041253329 |
Real period |
R |
1.8914176327673 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4017b1 |
Quadratic twists by: -3 |