Atkin-Lehner |
2- 3- 5- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
43680cj |
Isogeny class |
Conductor |
43680 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
617174649000000 = 26 · 32 · 56 · 74 · 134 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- 0 13+ 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-21770,-323400] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:630:1] |
Generators of the group modulo torsion |
j |
17829492203214784/9643353890625 |
j-invariant |
L |
8.453886603342 |
L(r)(E,1)/r! |
Ω |
0.41883715860305 |
Real period |
R |
1.682015398604 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000009 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
43680d1 87360q2 |
Quadratic twists by: -4 8 |