Atkin-Lehner |
2+ 3+ 17- 67- |
Signs for the Atkin-Lehner involutions |
Class |
27336d |
Isogeny class |
Conductor |
27336 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
21120 |
Modular degree for the optimal curve |
Δ |
-163816556544 = -1 · 211 · 35 · 173 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ -1 2 0 2 17- -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2856,-60948] |
[a1,a2,a3,a4,a6] |
Generators |
[77:412:1] |
Generators of the group modulo torsion |
j |
-1258404968018/79988553 |
j-invariant |
L |
4.5685707842889 |
L(r)(E,1)/r! |
Ω |
0.32532984192185 |
Real period |
R |
4.6809629239673 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
54672g1 82008p1 |
Quadratic twists by: -4 -3 |