Atkin-Lehner |
2+ 3- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744bj |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
34560 |
Modular degree for the optimal curve |
Δ |
2236272192 = 26 · 33 · 76 · 11 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 11+ -4 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4818,-130320] |
[a1,a2,a3,a4,a6] |
Generators |
[81:132:1] |
Generators of the group modulo torsion |
j |
1643032000/297 |
j-invariant |
L |
6.9911539230173 |
L(r)(E,1)/r! |
Ω |
0.57303355707018 |
Real period |
R |
4.0667507377872 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000059 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51744cb1 103488bp1 1056a1 |
Quadratic twists by: -4 8 -7 |