Atkin-Lehner |
2+ 3+ 19- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
81168m |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
7 |
Product of Tamagawa factors cp |
deg |
188160 |
Modular degree for the optimal curve |
Δ |
3818620069008 = 24 · 3 · 197 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -4 2 -7 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4112,39627] |
[a1,a2,a3,a4,a6] |
Generators |
[-17:323:1] [1503:58197:1] |
Generators of the group modulo torsion |
j |
480693953728768/238663754313 |
j-invariant |
L |
9.3317562387103 |
L(r)(E,1)/r! |
Ω |
0.69620640424428 |
Real period |
R |
1.9148172524511 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999907 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40584y1 |
Quadratic twists by: -4 |