Atkin-Lehner |
2+ 3- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
68952n |
Isogeny class |
Conductor |
68952 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
387072 |
Modular degree for the optimal curve |
Δ |
35746664518448208 = 24 · 36 · 139 · 172 |
Discriminant |
Eigenvalues |
2+ 3- 2 2 0 13+ 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-97907,7470282] |
[a1,a2,a3,a4,a6] |
Generators |
[1057:32955:1] |
Generators of the group modulo torsion |
j |
1343969093632/462866157 |
j-invariant |
L |
10.469737226273 |
L(r)(E,1)/r! |
Ω |
0.33694140869252 |
Real period |
R |
1.2947029952793 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000616 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5304l1 |
Quadratic twists by: 13 |