Atkin-Lehner |
2+ 3- 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
38304g |
Isogeny class |
Conductor |
38304 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
57466801728 = 26 · 39 · 74 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 0 7+ 0 -4 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1245,12364] |
[a1,a2,a3,a4,a6] |
Generators |
[-206:1323:8] [-7:144:1] |
Generators of the group modulo torsion |
j |
4574296000/1231713 |
j-invariant |
L |
8.7841432362587 |
L(r)(E,1)/r! |
Ω |
1.0403202504636 |
Real period |
R |
2.1109228702277 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38304bn1 76608bo1 12768t1 |
Quadratic twists by: -4 8 -3 |