Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744q |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
-6623232 = -1 · 212 · 3 · 72 · 11 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- 11- 0 5 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,47,1] |
[a1,a2,a3,a4,a6] |
Generators |
[0:1:1] |
Generators of the group modulo torsion |
j |
56000/33 |
j-invariant |
L |
5.5573402078201 |
L(r)(E,1)/r! |
Ω |
1.4421075041909 |
Real period |
R |
1.9268120412866 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000019 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744bh1 103488hj1 51744bc1 |
Quadratic twists by: -4 8 -7 |