Atkin-Lehner |
2- 3- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
6768q |
Isogeny class |
Conductor |
6768 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
236825856 = 28 · 39 · 47 |
Discriminant |
Eigenvalues |
2- 3- 3 1 -3 -4 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-336,2252] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:54:1] |
Generators of the group modulo torsion |
j |
22478848/1269 |
j-invariant |
L |
4.8347897101842 |
L(r)(E,1)/r! |
Ω |
1.7344177454853 |
Real period |
R |
0.34844472466114 |
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 |
1692d1 27072cf1 2256k1 |
Quadratic twists by: -4 8 -3 |