Atkin-Lehner |
2- 3- 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744cg |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
180 |
Product of Tamagawa factors cp |
deg |
207360 |
Modular degree for the optimal curve |
Δ |
-3180800544768 = -1 · 212 · 35 · 74 · 113 |
Discriminant |
Eigenvalues |
2- 3- -4 7+ 11- -4 -7 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-11825,498399] |
[a1,a2,a3,a4,a6] |
Generators |
[79:-252:1] [-110:693:1] |
Generators of the group modulo torsion |
j |
-18595667776/323433 |
j-invariant |
L |
9.0359879987617 |
L(r)(E,1)/r! |
Ω |
0.79866304150038 |
Real period |
R |
0.062854959748942 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999961 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744bt1 103488ew1 51744cd1 |
Quadratic twists by: -4 8 -7 |