Atkin-Lehner |
3+ 17+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
40749a |
Isogeny class |
Conductor |
40749 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
405504 |
Modular degree for the optimal curve |
Δ |
58079521659838869 = 311 · 178 · 47 |
Discriminant |
Eigenvalues |
0 3+ 1 -3 -1 -6 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-506135,138278009] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:11993:1] |
Generators of the group modulo torsion |
j |
594059784454144/2406187701 |
j-invariant |
L |
2.5624692254496 |
L(r)(E,1)/r! |
Ω |
0.35371953458413 |
Real period |
R |
3.6221765762314 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999898 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122247m1 2397d1 |
Quadratic twists by: -3 17 |