Atkin-Lehner |
2- 3- 7- 17+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
41412k |
Isogeny class |
Conductor |
41412 |
Conductor |
∏ cp |
216 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-172969024064256 = -1 · 28 · 39 · 74 · 17 · 292 |
Discriminant |
Eigenvalues |
2- 3- -3 7- -5 -5 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-13837,885839] |
[a1,a2,a3,a4,a6] |
Generators |
[-55:-1218:1] [-139:378:1] |
Generators of the group modulo torsion |
j |
-1144566302875648/675660250251 |
j-invariant |
L |
8.9786504818307 |
L(r)(E,1)/r! |
Ω |
0.52970159857411 |
Real period |
R |
0.078474043530682 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999988 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
124236y1 |
Quadratic twists by: -3 |