Atkin-Lehner |
2+ 3- 23- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
12282d |
Isogeny class |
Conductor |
12282 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
235872 |
Modular degree for the optimal curve |
Δ |
1663145850401980416 = 221 · 318 · 23 · 89 |
Discriminant |
Eigenvalues |
2+ 3- -1 2 -2 5 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-529784,-134873530] |
[a1,a2,a3,a4,a6] |
Generators |
[-372:3466:1] |
Generators of the group modulo torsion |
j |
16444438457275531713529/1663145850401980416 |
j-invariant |
L |
4.2756095128686 |
L(r)(E,1)/r! |
Ω |
0.17811373969672 |
Real period |
R |
1.3336077398099 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
98256j1 36846t1 |
Quadratic twists by: -4 -3 |