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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 38720z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38720.dg2 | 38720z1 | \([0, -1, 0, 1775, -668655]\) | \(16/5\) | \(-193163074846720\) | \([2]\) | \(101376\) | \(1.4204\) | \(\Gamma_0(N)\)-optimal |
| 38720.dg1 | 38720z2 | \([0, -1, 0, -104705, -12658303]\) | \(821516/25\) | \(3863261496934400\) | \([2]\) | \(202752\) | \(1.7669\) |
Rank
sage: E.rank()
The elliptic curves in class 38720z have rank \(0\).
Complex multiplication
The elliptic curves in class 38720z do not have complex multiplication.Modular form 38720.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
