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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 9408cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9408.ca2 | 9408cy1 | \([0, 1, 0, -1829, -25509]\) | \(16384/3\) | \(123966280704\) | \([2]\) | \(10752\) | \(0.84717\) | \(\Gamma_0(N)\)-optimal |
9408.ca1 | 9408cy2 | \([0, 1, 0, -8689, 285935]\) | \(109744/9\) | \(5950381473792\) | \([2]\) | \(21504\) | \(1.1937\) |
Rank
sage: E.rank()
The elliptic curves in class 9408cy have rank \(0\).
Complex multiplication
The elliptic curves in class 9408cy do not have complex multiplication.Modular form 9408.2.a.cy
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.