Atkin-Lehner |
3+ 7- 11- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
73689m |
Isogeny class |
Conductor |
73689 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
2883847974777 = 36 · 7 · 117 · 29 |
Discriminant |
Eigenvalues |
1 3+ -2 7- 11- -2 -2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1050510386,-13105788184089] |
[a1,a2,a3,a4,a6] |
Generators |
[-7314945340505501737117906737408028530283591444213898127411280:3657466435869439404448200973186942377014353790833914244853443:390896576805245284136242459067892332695726187044777472000] |
Generators of the group modulo torsion |
j |
72371679832051361738355457/1627857 |
j-invariant |
L |
4.6610893810842 |
L(r)(E,1)/r! |
Ω |
0.026518531271646 |
Real period |
R |
87.88362626925 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999959464 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6699d4 |
Quadratic twists by: -11 |