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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 116160et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.jo3 | 116160et1 | \([0, 1, 0, -108940, -13876150]\) | \(1261112198464/675\) | \(76531435200\) | \([2]\) | \(491520\) | \(1.4180\) | \(\Gamma_0(N)\)-optimal |
| 116160.jo2 | 116160et2 | \([0, 1, 0, -109545, -13714857]\) | \(20034997696/455625\) | \(3306158000640000\) | \([2, 2]\) | \(983040\) | \(1.7646\) | |
| 116160.jo4 | 116160et3 | \([0, 1, 0, 11455, -42246657]\) | \(2863288/13286025\) | \(-771260538389299200\) | \([2]\) | \(1966080\) | \(2.1112\) | |
| 116160.jo1 | 116160et4 | \([0, 1, 0, -240225, 25149375]\) | \(26410345352/10546875\) | \(612251481600000000\) | \([2]\) | \(1966080\) | \(2.1112\) |
Rank
sage: E.rank()
The elliptic curves in class 116160et have rank \(0\).
Complex multiplication
The elliptic curves in class 116160et do not have complex multiplication.Modular form 116160.2.a.et
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 Cremona 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 Cremona labels.
