Atkin-Lehner |
2- 3- 5+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
33930x |
Isogeny class |
Conductor |
33930 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
4080720384000 = 212 · 36 · 53 · 13 · 292 |
Discriminant |
Eigenvalues |
2- 3- 5+ 0 -2 13+ 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-5873,-141919] |
[a1,a2,a3,a4,a6] |
Generators |
[-57:100:1] |
Generators of the group modulo torsion |
j |
30726058889161/5597696000 |
j-invariant |
L |
8.2318528807909 |
L(r)(E,1)/r! |
Ω |
0.55221122482829 |
Real period |
R |
1.2422560593171 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3770b1 |
Quadratic twists by: -3 |