Atkin-Lehner |
3- 7+ 13+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
48321f |
Isogeny class |
Conductor |
48321 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
288000 |
Modular degree for the optimal curve |
Δ |
-16585366578083667 = -1 · 37 · 75 · 133 · 593 |
Discriminant |
Eigenvalues |
1 3- 2 7+ -4 13+ 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,22869,-6057180] |
[a1,a2,a3,a4,a6] |
Generators |
[1134:495:8] |
Generators of the group modulo torsion |
j |
1814374882538063/22750845786123 |
j-invariant |
L |
6.8068079037642 |
L(r)(E,1)/r! |
Ω |
0.19181900024701 |
Real period |
R |
2.9571314168516 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000015 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16107c1 |
Quadratic twists by: -3 |