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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 203280cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203280.ds2 | 203280cq1 | \([0, -1, 0, -17308485, 32463967725]\) | \(-79028701534867456/16987307596875\) | \(-123265235491338124800000\) | \([]\) | \(28800000\) | \(3.1519\) | \(\Gamma_0(N)\)-optimal |
203280.ds1 | 203280cq2 | \([0, -1, 0, -51866085, -2718075836595]\) | \(-2126464142970105856/438611057788643355\) | \(-3182699496026549496328826880\) | \([]\) | \(144000000\) | \(3.9566\) |
Rank
sage: E.rank()
The elliptic curves in class 203280cq have rank \(1\).
Complex multiplication
The elliptic curves in class 203280cq do not have complex multiplication.Modular form 203280.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.