Atkin-Lehner |
2+ 3+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61152a |
Isogeny class |
Conductor |
61152 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2042880 |
Modular degree for the optimal curve |
Δ |
-710143389176352768 = -1 · 212 · 34 · 78 · 135 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7+ 3 13+ 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-10205393,12551993889] |
[a1,a2,a3,a4,a6] |
Generators |
[2375:41292:1] |
Generators of the group modulo torsion |
j |
-4978158127432000/30074733 |
j-invariant |
L |
5.3281602525787 |
L(r)(E,1)/r! |
Ω |
0.25441331187198 |
Real period |
R |
5.2357325695974 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000281 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61152bp1 122304ck1 61152u1 |
Quadratic twists by: -4 8 -7 |