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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 18928.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18928.bf1 | 18928bb3 | \([0, -1, 0, -317269, 169633437]\) | \(-178643795968/524596891\) | \(-10371600362908954624\) | \([]\) | \(435456\) | \(2.3357\) | |
| 18928.bf2 | 18928bb1 | \([0, -1, 0, -19829, -1070083]\) | \(-43614208/91\) | \(-1799125479424\) | \([]\) | \(48384\) | \(1.2371\) | \(\Gamma_0(N)\)-optimal |
| 18928.bf3 | 18928bb2 | \([0, -1, 0, 34251, -5353219]\) | \(224755712/753571\) | \(-14898558095110144\) | \([]\) | \(145152\) | \(1.7864\) |
Rank
sage: E.rank()
The elliptic curves in class 18928.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 18928.bf do not have complex multiplication.Modular form 18928.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
