Atkin-Lehner |
2+ 3- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
51714j |
Isogeny class |
Conductor |
51714 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
449280 |
Modular degree for the optimal curve |
Δ |
-2587993811290368 = -1 · 28 · 36 · 138 · 17 |
Discriminant |
Eigenvalues |
2+ 3- -4 -1 -4 13+ 17- 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,34191,254749] |
[a1,a2,a3,a4,a6] |
Generators |
[66:1639:1] |
Generators of the group modulo torsion |
j |
7433231/4352 |
j-invariant |
L |
2.2247386240818 |
L(r)(E,1)/r! |
Ω |
0.27635230127478 |
Real period |
R |
4.0251856304664 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5746h1 51714x1 |
Quadratic twists by: -3 13 |