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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 242760da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242760.da4 | 242760da1 | \([0, 1, 0, 2505, -397482]\) | \(4499456/180075\) | \(-69545163802800\) | \([2]\) | \(589824\) | \(1.3359\) | \(\Gamma_0(N)\)-optimal |
| 242760.da3 | 242760da2 | \([0, 1, 0, -68300, -6600000]\) | \(5702413264/275625\) | \(1703146868640000\) | \([2, 2]\) | \(1179648\) | \(1.6825\) | |
| 242760.da2 | 242760da3 | \([0, 1, 0, -189680, 23210928]\) | \(30534944836/8203125\) | \(202755579600000000\) | \([2]\) | \(2359296\) | \(2.0291\) | |
| 242760.da1 | 242760da4 | \([0, 1, 0, -1079800, -432239200]\) | \(5633270409316/14175\) | \(350361641548800\) | \([2]\) | \(2359296\) | \(2.0291\) |
Rank
sage: E.rank()
The elliptic curves in class 242760da have rank \(1\).
Complex multiplication
The elliptic curves in class 242760da do not have complex multiplication.Modular form 242760.2.a.da
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.
