Atkin-Lehner |
2+ 3+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
24768f |
Isogeny class |
Conductor |
24768 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
-304349184 = -1 · 218 · 33 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -3 -3 5 -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-108,944] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:32:1] [-8:36:1] |
Generators of the group modulo torsion |
j |
-19683/43 |
j-invariant |
L |
7.0953383887924 |
L(r)(E,1)/r! |
Ω |
1.5312578935801 |
Real period |
R |
0.57920831123056 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24768bm1 387c1 24768e1 |
Quadratic twists by: -4 8 -3 |