Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368dw |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1769472 |
Modular degree for the optimal curve |
Δ |
-1305602420839022592 = -1 · 234 · 312 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- 4 0 11+ 13+ 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1325388,-589870960] |
[a1,a2,a3,a4,a6] |
Generators |
[23449828361707339412730:159015824448004965515264:17362007792063605125] |
Generators of the group modulo torsion |
j |
-1347365318848849/6831931392 |
j-invariant |
L |
9.0842593755101 |
L(r)(E,1)/r! |
Ω |
0.070331858693928 |
Real period |
R |
32.290698490951 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000213 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368ca1 20592by1 27456bt1 |
Quadratic twists by: -4 8 -3 |