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SageMath
sage: E = EllipticCurve("c1")
sage: E.isogeny_class()
Elliptic curves in class 121c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
121.c2 | 121c1 | [1, 1, 0, -2, -7] | [] | 6 | \(\Gamma_0(N)\)-optimal |
121.c1 | 121c2 | [1, 1, 0, -3632, 82757] | [] | 66 |
Rank
sage: E.rank()
The elliptic curves in class 121c have rank \(0\).
Complex multiplication
The elliptic curves in class 121c do not have complex multiplication.Modular form 121.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.