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SageMath
E = EllipticCurve("kq1")
E.isogeny_class()
Elliptic curves in class 235200.kq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.kq1 | 235200kq1 | \([0, -1, 0, -138833, 14655537]\) | \(78608/21\) | \(79060128000000000\) | \([2]\) | \(1966080\) | \(1.9507\) | \(\Gamma_0(N)\)-optimal |
235200.kq2 | 235200kq2 | \([0, -1, 0, 351167, 94525537]\) | \(318028/441\) | \(-6641050752000000000\) | \([2]\) | \(3932160\) | \(2.2973\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.kq have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.kq do not have complex multiplication.Modular form 235200.2.a.kq
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.