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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 94864cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94864.cx2 | 94864cq1 | \([0, -1, 0, -23536, -1382016]\) | \(-24729001\) | \(-58308726784\) | \([]\) | \(138240\) | \(1.1481\) | \(\Gamma_0(N)\)-optimal |
94864.cx1 | 94864cq2 | \([0, -1, 0, -239136, 176030912]\) | \(-121\) | \(-12498993425952968704\) | \([]\) | \(1520640\) | \(2.3471\) |
Rank
sage: E.rank()
The elliptic curves in class 94864cq have rank \(0\).
Complex multiplication
The elliptic curves in class 94864cq do not have complex multiplication.Modular form 94864.2.a.cq
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.