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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 267696cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 267696.cl1 | 267696cl1 | \([0, 0, 0, -140525823243, 20297554761233594]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-377775665119706899510685326639104\) | \([]\) | \(1137991680\) | \(5.1607\) | \(\Gamma_0(N)\)-optimal |
| 267696.cl2 | 267696cl2 | \([0, 0, 0, 397968773397, -1273866033923613286]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-705055295520104950391551286729211961344\) | \([]\) | \(7965941760\) | \(6.1337\) |
Rank
sage: E.rank()
The elliptic curves in class 267696cl have rank \(1\).
Complex multiplication
The elliptic curves in class 267696cl do not have complex multiplication.Modular form 267696.2.a.cl
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
