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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 243360cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 243360.cq3 | 243360cq1 | \([0, 0, 0, -344253, -76200748]\) | \(20034997696/455625\) | \(102606568070760000\) | \([2, 2]\) | \(2949120\) | \(2.0508\) | \(\Gamma_0(N)\)-optimal |
| 243360.cq2 | 243360cq2 | \([0, 0, 0, -754923, 140550878]\) | \(26410345352/10546875\) | \(19001216309400000000\) | \([2]\) | \(5898240\) | \(2.3974\) | |
| 243360.cq4 | 243360cq3 | \([0, 0, 0, 35997, -235373398]\) | \(2863288/13286025\) | \(-23936060199546892800\) | \([2]\) | \(5898240\) | \(2.3974\) | |
| 243360.cq1 | 243360cq4 | \([0, 0, 0, -5477628, -4934426848]\) | \(1261112198464/675\) | \(9728622750412800\) | \([2]\) | \(5898240\) | \(2.3974\) |
Rank
sage: E.rank()
The elliptic curves in class 243360cq have rank \(1\).
Complex multiplication
The elliptic curves in class 243360cq do not have complex multiplication.Modular form 243360.2.a.cq
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
