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SageMath
sage: E = EllipticCurve("ca1")
sage: E.isogeny_class()
Elliptic curves in class 15680ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
15680.p2 | 15680ca1 | [0, 1, 0, 51679, -5942945] | [] | 112896 | \(\Gamma_0(N)\)-optimal |
15680.p1 | 15680ca2 | [0, 1, 0, -497121, 234102175] | [] | 338688 |
Rank
sage: E.rank()
The elliptic curves in class 15680ca have rank \(0\).
Complex multiplication
The elliptic curves in class 15680ca do not have complex multiplication.Modular form 15680.2.a.ca
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.