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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 116281.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116281.d1 | 116281d3 | \([0, 1, 1, -909356180, -10555082202197]\) | \(-52893159101157376/11\) | \(-17294935994776451\) | \([]\) | \(17550000\) | \(3.4127\) | |
| 116281.d2 | 116281d2 | \([0, 1, 1, -1201570, -918633897]\) | \(-122023936/161051\) | \(-253215157899522019091\) | \([]\) | \(3510000\) | \(2.6079\) | |
| 116281.d3 | 116281d1 | \([0, 1, 1, -38760, 6962863]\) | \(-4096/11\) | \(-17294935994776451\) | \([]\) | \(702000\) | \(1.8032\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116281.d have rank \(1\).
Complex multiplication
The elliptic curves in class 116281.d do not have complex multiplication.Modular form 116281.2.a.d
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
