Atkin-Lehner |
2+ 3+ 7+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
12054a |
Isogeny class |
Conductor |
12054 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
-15947442 = -1 · 2 · 34 · 74 · 41 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7+ 2 -5 -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-25,-209] |
[a1,a2,a3,a4,a6] |
Generators |
[7:1:1] |
Generators of the group modulo torsion |
j |
-765625/6642 |
j-invariant |
L |
2.5317531660013 |
L(r)(E,1)/r! |
Ω |
0.93158333502833 |
Real period |
R |
1.3588441692789 |
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 |
96432cd1 36162bx1 12054p1 |
Quadratic twists by: -4 -3 -7 |