Atkin-Lehner |
2+ 3+ 13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
83304a |
Isogeny class |
Conductor |
83304 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-23319788544 = -1 · 210 · 39 · 13 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ -1 5 -3 13+ 2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1323,19926] |
[a1,a2,a3,a4,a6] |
Generators |
[63:432:1] |
Generators of the group modulo torsion |
j |
-12706092/1157 |
j-invariant |
L |
7.0717593766328 |
L(r)(E,1)/r! |
Ω |
1.1741839953517 |
Real period |
R |
1.5056753034988 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003358 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
83304n1 |
Quadratic twists by: -3 |