Atkin-Lehner |
2- 5+ 31+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
50840g |
Isogeny class |
Conductor |
50840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-5084000000 = -1 · 28 · 56 · 31 · 41 |
Discriminant |
Eigenvalues |
2- 0 5+ -2 -4 6 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,257,3042] |
[a1,a2,a3,a4,a6] |
Generators |
[-7:30:1] [7:72:1] |
Generators of the group modulo torsion |
j |
7333024176/19859375 |
j-invariant |
L |
8.3349745546074 |
L(r)(E,1)/r! |
Ω |
0.95648676390229 |
Real period |
R |
4.3570778337816 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999989 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
101680b1 |
Quadratic twists by: -4 |