Atkin-Lehner |
2+ 3+ 5- 17- |
Signs for the Atkin-Lehner involutions |
Class |
24480f |
Isogeny class |
Conductor |
24480 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-459000000 = -1 · 26 · 33 · 56 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -4 -4 2 17- -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-57,1044] |
[a1,a2,a3,a4,a6] |
Generators |
[3:30:1] |
Generators of the group modulo torsion |
j |
-11852352/265625 |
j-invariant |
L |
4.4036944358748 |
L(r)(E,1)/r! |
Ω |
1.3987008393517 |
Real period |
R |
0.52473627812077 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24480ba1 48960o2 24480v1 122400cf1 |
Quadratic twists by: -4 8 -3 5 |