Atkin-Lehner |
2+ 3- 5- 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
54990w |
Isogeny class |
Conductor |
54990 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
739200 |
Modular degree for the optimal curve |
Δ |
-86995898437500000 = -1 · 25 · 36 · 514 · 13 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 4 13- -7 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-72189,16052773] |
[a1,a2,a3,a4,a6] |
Generators |
[-313:2969:1] |
Generators of the group modulo torsion |
j |
-57070627168555729/119335937500000 |
j-invariant |
L |
4.7170810798424 |
L(r)(E,1)/r! |
Ω |
0.30266162548506 |
Real period |
R |
0.55661890122417 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000162 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6110c1 |
Quadratic twists by: -3 |