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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 41616.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41616.cu1 | 41616cw2 | \([0, 0, 0, -5415241251, -153382152309982]\) | \(-843137281012581793/216\) | \(-4499172023048699904\) | \([]\) | \(22208256\) | \(3.8616\) | |
| 41616.cu2 | 41616cw1 | \([0, 0, 0, -66752931, -211074104158]\) | \(-1579268174113/10077696\) | \(-209913369907360142721024\) | \([]\) | \(7402752\) | \(3.3123\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41616.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 41616.cu do not have complex multiplication.Modular form 41616.2.a.cu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
