Atkin-Lehner |
2+ 3- 19+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
81168y |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
23808 |
Modular degree for the optimal curve |
Δ |
-87904944 = -1 · 24 · 32 · 193 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 3 0 1 -1 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-299,1944] |
[a1,a2,a3,a4,a6] |
Generators |
[-20:18:1] |
Generators of the group modulo torsion |
j |
-185382602752/5494059 |
j-invariant |
L |
10.848523012892 |
L(r)(E,1)/r! |
Ω |
1.9052955036666 |
Real period |
R |
2.8469397506588 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000564 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40584d1 |
Quadratic twists by: -4 |