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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 262392.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262392.bf1 | 262392bf1 | \([0, 1, 0, -2803, -27130]\) | \(256000/117\) | \(1113509256912\) | \([2]\) | \(358400\) | \(1.0065\) | \(\Gamma_0(N)\)-optimal |
262392.bf2 | 262392bf2 | \([0, 1, 0, 9812, -193648]\) | \(686000/507\) | \(-77203308479232\) | \([2]\) | \(716800\) | \(1.3530\) |
Rank
sage: E.rank()
The elliptic curves in class 262392.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 262392.bf do not have complex multiplication.Modular form 262392.2.a.bf
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.