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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 301392de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301392.de4 | 301392de1 | \([0, 0, 0, -1314, 31995]\) | \(-21511084032/25465531\) | \(-297029953584\) | \([2]\) | \(262144\) | \(0.89535\) | \(\Gamma_0(N)\)-optimal |
| 301392.de3 | 301392de2 | \([0, 0, 0, -25119, 1531710]\) | \(9392111857872/4380649\) | \(817534238976\) | \([2, 2]\) | \(524288\) | \(1.2419\) | |
| 301392.de1 | 301392de3 | \([0, 0, 0, -401859, 98052498]\) | \(9614292367656708/2093\) | \(1562416128\) | \([2]\) | \(1048576\) | \(1.5885\) | |
| 301392.de2 | 301392de4 | \([0, 0, 0, -29259, 992682]\) | \(3710860803108/1577224103\) | \(1177391483993088\) | \([2]\) | \(1048576\) | \(1.5885\) |
Rank
sage: E.rank()
The elliptic curves in class 301392de have rank \(1\).
Complex multiplication
The elliptic curves in class 301392de do not have complex multiplication.Modular form 301392.2.a.de
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.
