Atkin-Lehner |
2- 3- 19- 89- |
Signs for the Atkin-Lehner involutions |
Class |
81168cs |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
4945920 |
Modular degree for the optimal curve |
Δ |
-493771567104 = -1 · 212 · 32 · 19 · 893 |
Discriminant |
Eigenvalues |
2- 3- 3 -4 5 -1 -1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-97767064,372047967188] |
[a1,a2,a3,a4,a6] |
Generators |
[5806:12816:1] |
Generators of the group modulo torsion |
j |
-25231408121333628493036057/120549699 |
j-invariant |
L |
9.3652590444594 |
L(r)(E,1)/r! |
Ω |
0.30475761100466 |
Real period |
R |
1.2804245494329 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002449 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5073d1 |
Quadratic twists by: -4 |