Atkin-Lehner |
2- 3+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
4128l |
Isogeny class |
Conductor |
4128 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
4224 |
Modular degree for the optimal curve |
Δ |
-2930946048 = -1 · 212 · 32 · 433 |
Discriminant |
Eigenvalues |
2- 3+ -4 -2 -1 -5 3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1565,24501] |
[a1,a2,a3,a4,a6] |
Generators |
[71:516:1] |
Generators of the group modulo torsion |
j |
-103558145536/715563 |
j-invariant |
L |
2.0166243707235 |
L(r)(E,1)/r! |
Ω |
1.4354440608542 |
Real period |
R |
0.11707320088365 |
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 |
4128c1 8256p1 12384i1 103200r1 |
Quadratic twists by: -4 8 -3 5 |