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SageMath
E = EllipticCurve("nz1")
E.isogeny_class()
Elliptic curves in class 352800.nz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 352800.nz1 | 352800nz4 | \([0, 0, 0, -12351675, -16708473250]\) | \(303735479048/105\) | \(72043541640000000\) | \([2]\) | \(14155776\) | \(2.5906\) | |
| 352800.nz2 | 352800nz2 | \([0, 0, 0, -1602300, 389648000]\) | \(82881856/36015\) | \(197687478260160000000\) | \([2]\) | \(14155776\) | \(2.5906\) | |
| 352800.nz3 | 352800nz1 | \([0, 0, 0, -775425, -258622000]\) | \(601211584/11025\) | \(945571484025000000\) | \([2, 2]\) | \(7077888\) | \(2.2440\) | \(\Gamma_0(N)\)-optimal |
| 352800.nz4 | 352800nz3 | \([0, 0, 0, -3675, -750226750]\) | \(-8/354375\) | \(-243146953035000000000\) | \([2]\) | \(14155776\) | \(2.5906\) |
Rank
sage: E.rank()
The elliptic curves in class 352800.nz have rank \(0\).
Complex multiplication
The elliptic curves in class 352800.nz do not have complex multiplication.Modular form 352800.2.a.nz
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
