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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 159120.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159120.ce1 | 159120eg4 | \([0, 0, 0, -812163, -210014638]\) | \(79364416584061444/20404090514925\) | \(15231571953029452800\) | \([2]\) | \(3145728\) | \(2.3902\) | |
| 159120.ce2 | 159120eg2 | \([0, 0, 0, -285663, 56078462]\) | \(13813960087661776/714574355625\) | \(133356724544160000\) | \([2, 2]\) | \(1572864\) | \(2.0436\) | |
| 159120.ce3 | 159120eg1 | \([0, 0, 0, -282018, 57645083]\) | \(212670222886967296/616241925\) | \(7187845813200\) | \([2]\) | \(786432\) | \(1.6970\) | \(\Gamma_0(N)\)-optimal |
| 159120.ce4 | 159120eg3 | \([0, 0, 0, 182517, 221907818]\) | \(900753985478876/29018422265625\) | \(-21662136147600000000\) | \([2]\) | \(3145728\) | \(2.3902\) |
Rank
sage: E.rank()
The elliptic curves in class 159120.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 159120.ce do not have complex multiplication.Modular form 159120.2.a.ce
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
