Atkin-Lehner |
2+ 3- 19+ 79+ |
Signs for the Atkin-Lehner involutions |
Class |
72048f |
Isogeny class |
Conductor |
72048 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
55552 |
Modular degree for the optimal curve |
Δ |
-63867958272 = -1 · 210 · 37 · 192 · 79 |
Discriminant |
Eigenvalues |
2+ 3- 0 -3 -1 -3 1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-168,12132] |
[a1,a2,a3,a4,a6] |
Generators |
[-24:54:1] [-9:114:1] |
Generators of the group modulo torsion |
j |
-515150500/62371053 |
j-invariant |
L |
11.670382574162 |
L(r)(E,1)/r! |
Ω |
0.90578505553105 |
Real period |
R |
0.46015263235336 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
36024b1 |
Quadratic twists by: -4 |