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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 72450.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.dv1 | 72450do4 | \([1, -1, 1, -108531005, 425935025997]\) | \(12411881707829361287041/303132494474220600\) | \(3452868569870419021875000\) | \([2]\) | \(23887872\) | \(3.4925\) | |
| 72450.dv2 | 72450do2 | \([1, -1, 1, -13356005, -18556524003]\) | \(23131609187144855041/322060536000000\) | \(3668470792875000000000\) | \([2]\) | \(7962624\) | \(2.9432\) | |
| 72450.dv3 | 72450do1 | \([1, -1, 1, -108005, -777708003]\) | \(-12232183057921/22933241856000\) | \(-261223958016000000000\) | \([2]\) | \(3981312\) | \(2.5966\) | \(\Gamma_0(N)\)-optimal |
| 72450.dv4 | 72450do3 | \([1, -1, 1, 971995, 20992931997]\) | \(8915971454369279/16719623332762560\) | \(-190446959524748535000000\) | \([2]\) | \(11943936\) | \(3.1459\) |
Rank
sage: E.rank()
The elliptic curves in class 72450.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 72450.dv do not have complex multiplication.Modular form 72450.2.a.dv
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
