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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 560.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
560.c1 | 560f2 | \([0, -1, 0, -805, 9065]\) | \(-225637236736/1715\) | \(-439040\) | \([]\) | \(144\) | \(0.25755\) | |
560.c2 | 560f1 | \([0, -1, 0, -5, 25]\) | \(-65536/875\) | \(-224000\) | \([]\) | \(48\) | \(-0.29176\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 560.c have rank \(1\).
Complex multiplication
The elliptic curves in class 560.c do not have complex multiplication.Modular form 560.2.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 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.