Atkin-Lehner |
2- 3+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
6768i |
Isogeny class |
Conductor |
6768 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
324864 = 28 · 33 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -3 -3 -1 -4 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-24,-36] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:3:1] [-2:2:1] |
Generators of the group modulo torsion |
j |
221184/47 |
j-invariant |
L |
4.4326573713828 |
L(r)(E,1)/r! |
Ω |
2.1894175955076 |
Real period |
R |
0.50614571889791 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999979 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1692b1 27072bn1 6768j1 |
Quadratic twists by: -4 8 -3 |