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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 18928bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18928.x1 | 18928bf1 | \([0, 1, 0, -44672, 3808052]\) | \(-226981/14\) | \(-608104412045312\) | \([]\) | \(74880\) | \(1.5912\) | \(\Gamma_0(N)\)-optimal |
| 18928.x2 | 18928bf2 | \([0, 1, 0, 131088, -231780652]\) | \(5735339/537824\) | \(-23360939093132705792\) | \([]\) | \(374400\) | \(2.3959\) |
Rank
sage: E.rank()
The elliptic curves in class 18928bf have rank \(0\).
Complex multiplication
The elliptic curves in class 18928bf 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 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.
