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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 16560.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16560.n1 | 16560bi4 | \([0, 0, 0, -15897603, 24397514498]\) | \(148809678420065817601/20700\) | \(61809868800\) | \([2]\) | \(294912\) | \(2.3955\) | |
| 16560.n2 | 16560bi5 | \([0, 0, 0, -3719523, -2365109278]\) | \(1905890658841300321/293666194803750\) | \(876882559024880640000\) | \([2]\) | \(589824\) | \(2.7420\) | |
| 16560.n3 | 16560bi3 | \([0, 0, 0, -1019523, 360270722]\) | \(39248884582600321/3935264062500\) | \(11750635526400000000\) | \([2, 2]\) | \(294912\) | \(2.3955\) | |
| 16560.n4 | 16560bi2 | \([0, 0, 0, -993603, 381208898]\) | \(36330796409313601/428490000\) | \(1279464284160000\) | \([2, 2]\) | \(147456\) | \(2.0489\) | |
| 16560.n5 | 16560bi1 | \([0, 0, 0, -60483, 6281282]\) | \(-8194759433281/965779200\) | \(-2883801238732800\) | \([2]\) | \(73728\) | \(1.7023\) | \(\Gamma_0(N)\)-optimal |
| 16560.n6 | 16560bi6 | \([0, 0, 0, 1265757, 1745607458]\) | \(75108181893694559/484313964843750\) | \(-1446153750000000000000\) | \([2]\) | \(589824\) | \(2.7420\) |
Rank
sage: E.rank()
The elliptic curves in class 16560.n have rank \(1\).
Complex multiplication
The elliptic curves in class 16560.n do not have complex multiplication.Modular form 16560.2.a.n
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
