Atkin-Lehner |
2+ 7+ 11- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
89782f |
Isogeny class |
Conductor |
89782 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
557568 |
Modular degree for the optimal curve |
Δ |
997588505010944 = 28 · 73 · 118 · 53 |
Discriminant |
Eigenvalues |
2+ -2 -3 7+ 11- 4 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-26260,-613230] |
[a1,a2,a3,a4,a6] |
Generators |
[-143:543:1] [-111:1023:1] |
Generators of the group modulo torsion |
j |
9342059353/4653824 |
j-invariant |
L |
4.8691763064091 |
L(r)(E,1)/r! |
Ω |
0.3948772137595 |
Real period |
R |
2.0551436142508 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001608 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89782bh1 |
Quadratic twists by: -11 |