Atkin-Lehner |
2+ 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48672j |
Isogeny class |
Conductor |
48672 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
107520 |
Modular degree for the optimal curve |
Δ |
-20723693432832 = -1 · 212 · 311 · 134 |
Discriminant |
Eigenvalues |
2+ 3- 0 1 -6 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-20280,1132976] |
[a1,a2,a3,a4,a6] |
Generators |
[-143:1053:1] [100:324:1] |
Generators of the group modulo torsion |
j |
-10816000/243 |
j-invariant |
L |
9.5347146405104 |
L(r)(E,1)/r! |
Ω |
0.6816610124239 |
Real period |
R |
0.58281135263291 |
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 |
48672k1 97344ej1 16224m1 48672bl1 |
Quadratic twists by: -4 8 -3 13 |