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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 23232dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23232.cw1 | 23232dl1 | \([0, 1, 0, -4033, 27839]\) | \(62500/33\) | \(3831333715968\) | \([2]\) | \(30720\) | \(1.1061\) | \(\Gamma_0(N)\)-optimal |
| 23232.cw2 | 23232dl2 | \([0, 1, 0, 15327, 233055]\) | \(1714750/1089\) | \(-252868025253888\) | \([2]\) | \(61440\) | \(1.4527\) |
Rank
sage: E.rank()
The elliptic curves in class 23232dl have rank \(0\).
Complex multiplication
The elliptic curves in class 23232dl do not have complex multiplication.Modular form 23232.2.a.dl
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.
