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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 142296h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142296.cs3 | 142296h1 | \([0, 1, 0, -73124, -7362720]\) | \(810448/33\) | \(1760752266991872\) | \([2]\) | \(737280\) | \(1.6912\) | \(\Gamma_0(N)\)-optimal |
| 142296.cs2 | 142296h2 | \([0, 1, 0, -191704, 22424576]\) | \(3650692/1089\) | \(232419299242927104\) | \([2, 2]\) | \(1474560\) | \(2.0377\) | |
| 142296.cs1 | 142296h3 | \([0, 1, 0, -2800464, 1802642400]\) | \(5690357426/891\) | \(380322489670244352\) | \([2]\) | \(2949120\) | \(2.3843\) | |
| 142296.cs4 | 142296h4 | \([0, 1, 0, 519776, 150490976]\) | \(36382894/43923\) | \(-18748490138929453056\) | \([2]\) | \(2949120\) | \(2.3843\) |
Rank
sage: E.rank()
The elliptic curves in class 142296h have rank \(1\).
Complex multiplication
The elliptic curves in class 142296h do not have complex multiplication.Modular form 142296.2.a.h
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.
