Atkin-Lehner |
2+ 3- 43- |
Signs for the Atkin-Lehner involutions |
Class |
4128f |
Isogeny class |
Conductor |
4128 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
-4755456 = -1 · 212 · 33 · 43 |
Discriminant |
Eigenvalues |
2+ 3- 1 1 -5 -5 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-65,207] |
[a1,a2,a3,a4,a6] |
Generators |
[7:-12:1] |
Generators of the group modulo torsion |
j |
-7529536/1161 |
j-invariant |
L |
4.4344230572364 |
L(r)(E,1)/r! |
Ω |
2.3538599770661 |
Real period |
R |
0.1569911797516 |
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 |
4128i1 8256d1 12384p1 103200bn1 |
Quadratic twists by: -4 8 -3 5 |