Atkin-Lehner |
2+ 3+ 5+ 7+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
48720d |
Isogeny class |
Conductor |
48720 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1290240 |
Modular degree for the optimal curve |
Δ |
6243201562500000000 = 28 · 39 · 514 · 7 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ -4 4 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1227716,-509197920] |
[a1,a2,a3,a4,a6] |
Generators |
[9703467193617619:-627951396821085202:2162202350491] |
Generators of the group modulo torsion |
j |
799425224942162511184/24387506103515625 |
j-invariant |
L |
3.9481741921733 |
L(r)(E,1)/r! |
Ω |
0.14369305598883 |
Real period |
R |
27.476443903496 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999935 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24360ba1 |
Quadratic twists by: -4 |