Atkin-Lehner |
2+ 13+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
12272b |
Isogeny class |
Conductor |
12272 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
-35542068224 = -1 · 210 · 132 · 593 |
Discriminant |
Eigenvalues |
2+ -1 -1 1 -4 13+ -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-536,10432] |
[a1,a2,a3,a4,a6] |
Generators |
[-28:52:1] [-18:118:1] |
Generators of the group modulo torsion |
j |
-16662038116/34709051 |
j-invariant |
L |
5.2239822804942 |
L(r)(E,1)/r! |
Ω |
1.0313463903763 |
Real period |
R |
0.21105026437773 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6136d1 49088r1 110448g1 |
Quadratic twists by: -4 8 -3 |