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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 159120.eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159120.eh1 | 159120x4 | \([0, 0, 0, -201387, -33549734]\) | \(302503589987689/12214946250\) | \(36473634063360000\) | \([2]\) | \(1572864\) | \(1.9440\) | |
| 159120.eh2 | 159120x2 | \([0, 0, 0, -32907, 1595194]\) | \(1319778683209/395612100\) | \(1181291400806400\) | \([2, 2]\) | \(786432\) | \(1.5975\) | |
| 159120.eh3 | 159120x1 | \([0, 0, 0, -30027, 2002426]\) | \(1002702430729/159120\) | \(475129774080\) | \([2]\) | \(393216\) | \(1.2509\) | \(\Gamma_0(N)\)-optimal |
| 159120.eh4 | 159120x3 | \([0, 0, 0, 89493, 10677274]\) | \(26546265663191/31856082570\) | \(-95121752856698880\) | \([2]\) | \(1572864\) | \(1.9440\) |
Rank
sage: E.rank()
The elliptic curves in class 159120.eh have rank \(0\).
Complex multiplication
The elliptic curves in class 159120.eh do not have complex multiplication.Modular form 159120.2.a.eh
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 LMFDB 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 LMFDB labels.
