Atkin-Lehner |
2+ 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
12272d |
Isogeny class |
Conductor |
12272 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7488 |
Modular degree for the optimal curve |
Δ |
-92678144 = -1 · 211 · 13 · 592 |
Discriminant |
Eigenvalues |
2+ 1 3 -3 2 13- -7 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3424,75988] |
[a1,a2,a3,a4,a6] |
Generators |
[6:236:1] |
Generators of the group modulo torsion |
j |
-2168312432834/45253 |
j-invariant |
L |
5.9823725451799 |
L(r)(E,1)/r! |
Ω |
1.7566257911441 |
Real period |
R |
0.42570055154459 |
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 |
6136f1 49088o1 110448t1 |
Quadratic twists by: -4 8 -3 |