Atkin-Lehner |
2- 3+ 19+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
81168bs |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
-26803779303112704 = -1 · 228 · 310 · 19 · 89 |
Discriminant |
Eigenvalues |
2- 3+ -1 -2 3 -7 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,52464,6358464] |
[a1,a2,a3,a4,a6] |
Generators |
[-40:2048:1] |
Generators of the group modulo torsion |
j |
3898878343727471/6543891431424 |
j-invariant |
L |
3.1603866514781 |
L(r)(E,1)/r! |
Ω |
0.25678078262724 |
Real period |
R |
1.5384653309129 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999928634 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10146r1 |
Quadratic twists by: -4 |