Atkin-Lehner |
13+ 17+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
83317a |
Isogeny class |
Conductor |
83317 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
67968 |
Modular degree for the optimal curve |
Δ |
-587253292457 = -1 · 132 · 173 · 294 |
Discriminant |
Eigenvalues |
1 -1 0 -3 4 13+ 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,1895,-17974] |
[a1,a2,a3,a4,a6] |
Generators |
[22:176:1] |
Generators of the group modulo torsion |
j |
4449451823375/3474871553 |
j-invariant |
L |
4.1056895242962 |
L(r)(E,1)/r! |
Ω |
0.51110510168031 |
Real period |
R |
4.0164826267473 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003932 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
83317b1 |
Quadratic twists by: 13 |