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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 33600cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33600.gb1 | 33600cx1 | \([0, 1, 0, -533, 1563]\) | \(1048576/525\) | \(8400000000\) | \([2]\) | \(18432\) | \(0.59708\) | \(\Gamma_0(N)\)-optimal |
33600.gb2 | 33600cx2 | \([0, 1, 0, 1967, 14063]\) | \(3286064/2205\) | \(-564480000000\) | \([2]\) | \(36864\) | \(0.94365\) |
Rank
sage: E.rank()
The elliptic curves in class 33600cx have rank \(1\).
Complex multiplication
The elliptic curves in class 33600cx do not have complex multiplication.Modular form 33600.2.a.cx
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.