Atkin-Lehner |
2+ 3+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
47424g |
Isogeny class |
Conductor |
47424 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
214272 |
Modular degree for the optimal curve |
Δ |
-112324739904 = -1 · 26 · 39 · 13 · 193 |
Discriminant |
Eigenvalues |
2+ 3+ -1 3 4 13+ 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-382676,-90988626] |
[a1,a2,a3,a4,a6] |
Generators |
[9481761696577656460686448477973114279:-560351268247222314832032727258163953588:2628967912864479071434621505194217] |
Generators of the group modulo torsion |
j |
-96836380962843416896/1755074061 |
j-invariant |
L |
5.7188264574515 |
L(r)(E,1)/r! |
Ω |
0.095975781589086 |
Real period |
R |
59.58614103229 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47424bi1 23712j1 |
Quadratic twists by: -4 8 |