Atkin-Lehner |
2- 3+ 5+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
12240bd |
Isogeny class |
Conductor |
12240 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-265302000 = -1 · 24 · 33 · 53 · 173 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 1 -3 -4 17- -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2493,-47917] |
[a1,a2,a3,a4,a6] |
Generators |
[58:51:1] |
Generators of the group modulo torsion |
j |
-3966493992192/614125 |
j-invariant |
L |
4.1061576194557 |
L(r)(E,1)/r! |
Ω |
0.33781968709492 |
Real period |
R |
2.0258132648448 |
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 |
3060c1 48960dw1 12240bh2 61200da1 |
Quadratic twists by: -4 8 -3 5 |