Atkin-Lehner |
2+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
21824c |
Isogeny class |
Conductor |
21824 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
4864 |
Modular degree for the optimal curve |
Δ |
-11173888 = -1 · 215 · 11 · 31 |
Discriminant |
Eigenvalues |
2+ 0 -2 -1 11+ 4 -3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-716,-7376] |
[a1,a2,a3,a4,a6] |
Generators |
[45:227:1] |
Generators of the group modulo torsion |
j |
-1238833224/341 |
j-invariant |
L |
3.7856431992582 |
L(r)(E,1)/r! |
Ω |
0.46146007473989 |
Real period |
R |
4.1018101093491 |
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 |
21824k1 10912b1 |
Quadratic twists by: -4 8 |