Atkin-Lehner |
2+ 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368s |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
884736 |
Modular degree for the optimal curve |
Δ |
-861901598132011008 = -1 · 226 · 312 · 11 · 133 |
Discriminant |
Eigenvalues |
2+ 3- 0 -4 11+ 13+ 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,207060,-26076112] |
[a1,a2,a3,a4,a6] |
j |
5137417856375/4510142208 |
j-invariant |
L |
0.61871590465678 |
L(r)(E,1)/r! |
Ω |
0.1546789828355 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368en1 2574x1 27456n1 |
Quadratic twists by: -4 8 -3 |