Atkin-Lehner |
2- 3+ 7- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
12054bc |
Isogeny class |
Conductor |
12054 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
72576 |
Modular degree for the optimal curve |
Δ |
-2084190842228544 = -1 · 26 · 39 · 79 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 3 7- -2 -1 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,31506,-424341] |
[a1,a2,a3,a4,a6] |
Generators |
[167:3003:1] |
Generators of the group modulo torsion |
j |
85707789929/51648192 |
j-invariant |
L |
7.02265424028 |
L(r)(E,1)/r! |
Ω |
0.27019277044152 |
Real period |
R |
2.1659394725244 |
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 |
96432co1 36162bj1 12054bo1 |
Quadratic twists by: -4 -3 -7 |