Atkin-Lehner |
2- 19+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
4712a |
Isogeny class |
Conductor |
4712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
640 |
Modular degree for the optimal curve |
Δ |
-4674304 = -1 · 28 · 19 · 312 |
Discriminant |
Eigenvalues |
2- 0 3 1 3 2 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-116,-492] |
[a1,a2,a3,a4,a6] |
j |
-674307072/18259 |
j-invariant |
L |
2.9048335433924 |
L(r)(E,1)/r! |
Ω |
0.72620838584811 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9424a1 37696c1 42408e1 117800a1 |
Quadratic twists by: -4 8 -3 5 |