Atkin-Lehner |
2+ 3- 19- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
80712g |
Isogeny class |
Conductor |
80712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
319488 |
Modular degree for the optimal curve |
Δ |
-286193129472 = -1 · 211 · 38 · 192 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 2 -1 3 1 -1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-703299,227016862] |
[a1,a2,a3,a4,a6] |
Generators |
[3858:589:8] |
Generators of the group modulo torsion |
j |
-25768327484921474/191691 |
j-invariant |
L |
8.2711734651304 |
L(r)(E,1)/r! |
Ω |
0.67233605338008 |
Real period |
R |
3.0755354490337 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000217 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
26904f1 |
Quadratic twists by: -3 |