Atkin-Lehner |
2- 3+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
51156b |
Isogeny class |
Conductor |
51156 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
108864 |
Modular degree for the optimal curve |
Δ |
-1074477963888 = -1 · 24 · 39 · 76 · 29 |
Discriminant |
Eigenvalues |
2- 3+ -4 7- -3 -5 -5 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1323,46305] |
[a1,a2,a3,a4,a6] |
Generators |
[-24:27:1] |
Generators of the group modulo torsion |
j |
6912/29 |
j-invariant |
L |
2.9553104099058 |
L(r)(E,1)/r! |
Ω |
0.62366958624561 |
Real period |
R |
2.3692917492264 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000012 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51156d1 1044b1 |
Quadratic twists by: -3 -7 |