Atkin-Lehner |
2- 3- 23+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
67896f |
Isogeny class |
Conductor |
67896 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
1769472 |
Modular degree for the optimal curve |
Δ |
-4677501730874717952 = -1 · 28 · 312 · 233 · 414 |
Discriminant |
Eigenvalues |
2- 3- 4 -2 4 -6 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-508143,173970290] |
[a1,a2,a3,a4,a6] |
Generators |
[3205:177390:1] |
Generators of the group modulo torsion |
j |
-77752445998933456/25063773849423 |
j-invariant |
L |
8.3296667774921 |
L(r)(E,1)/r! |
Ω |
0.2307613739871 |
Real period |
R |
4.5120564552218 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000693 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22632a1 |
Quadratic twists by: -3 |