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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 260100cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
260100.cu2 | 260100cu1 | \([0, 0, 0, 758625, 67553750]\) | \(27440/17\) | \(-29913689261700000000\) | \([]\) | \(3110400\) | \(2.4262\) | \(\Gamma_0(N)\)-optimal |
260100.cu1 | 260100cu2 | \([0, 0, 0, -12246375, 17091098750]\) | \(-115431760/4913\) | \(-8645056196631300000000\) | \([]\) | \(9331200\) | \(2.9755\) |
Rank
sage: E.rank()
The elliptic curves in class 260100cu have rank \(0\).
Complex multiplication
The elliptic curves in class 260100cu do not have complex multiplication.Modular form 260100.2.a.cu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.