Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744u |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
401783570496 = 26 · 32 · 78 · 112 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- 11- 2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2662,44080] |
[a1,a2,a3,a4,a6] |
Generators |
[-56:120:1] |
Generators of the group modulo torsion |
j |
277167808/53361 |
j-invariant |
L |
6.3971196579154 |
L(r)(E,1)/r! |
Ω |
0.89940777386938 |
Real period |
R |
3.5562955112043 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000012 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
51744bn1 103488hw2 7392h1 |
Quadratic twists by: -4 8 -7 |