Atkin-Lehner |
2+ 3- 5- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
75240y |
Isogeny class |
Conductor |
75240 |
Conductor |
∏ cp |
224 |
Product of Tamagawa factors cp |
deg |
1204224 |
Modular degree for the optimal curve |
Δ |
129324207251250000 = 24 · 38 · 57 · 112 · 194 |
Discriminant |
Eigenvalues |
2+ 3- 5- 2 11- 4 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2097462,1169073209] |
[a1,a2,a3,a4,a6] |
Generators |
[-1052:47025:1] |
Generators of the group modulo torsion |
j |
87490017893914691584/11087466328125 |
j-invariant |
L |
8.2868642264191 |
L(r)(E,1)/r! |
Ω |
0.31708868548813 |
Real period |
R |
0.46668243023123 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999087 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25080k1 |
Quadratic twists by: -3 |