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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 310464dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.dh3 | 310464dh1 | \([0, 0, 0, -21756, 1190896]\) | \(810448/33\) | \(46371340173312\) | \([2]\) | \(786432\) | \(1.3881\) | \(\Gamma_0(N)\)-optimal |
| 310464.dh2 | 310464dh2 | \([0, 0, 0, -57036, -3649520]\) | \(3650692/1089\) | \(6121016902877184\) | \([2, 2]\) | \(1572864\) | \(1.7347\) | |
| 310464.dh4 | 310464dh3 | \([0, 0, 0, 154644, -24394160]\) | \(36382894/43923\) | \(-493762030165426176\) | \([2]\) | \(3145728\) | \(2.0812\) | |
| 310464.dh1 | 310464dh4 | \([0, 0, 0, -833196, -292691504]\) | \(5690357426/891\) | \(10016209477435392\) | \([2]\) | \(3145728\) | \(2.0812\) |
Rank
sage: E.rank()
The elliptic curves in class 310464dh have rank \(0\).
Complex multiplication
The elliptic curves in class 310464dh do not have complex multiplication.Modular form 310464.2.a.dh
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.
