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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 301530z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301530.z2 | 301530z1 | \([1, 0, 1, -1897799, -1244078278]\) | \(-419685050303/128250000\) | \(-230997828832629750000\) | \([2]\) | \(11446272\) | \(2.6212\) | \(\Gamma_0(N)\)-optimal |
| 301530.z1 | 301530z2 | \([1, 0, 1, -32315299, -70705481278]\) | \(2072037945890303/131584500\) | \(237003772382278123500\) | \([2]\) | \(22892544\) | \(2.9678\) |
Rank
sage: E.rank()
The elliptic curves in class 301530z have rank \(1\).
Complex multiplication
The elliptic curves in class 301530z do not have complex multiplication.Modular form 301530.2.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.
