Atkin-Lehner |
2+ 3+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
5586f |
Isogeny class |
Conductor |
5586 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
84119976192 = 28 · 3 · 78 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ -4 7- -2 0 -8 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1887,27525] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:249:1] [-1:172:1] |
Generators of the group modulo torsion |
j |
6321363049/715008 |
j-invariant |
L |
2.8176693511813 |
L(r)(E,1)/r! |
Ω |
1.0446954982844 |
Real period |
R |
1.3485601095293 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999963 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
44688du1 16758bj1 798f1 106134di1 |
Quadratic twists by: -4 -3 -7 -19 |