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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 164730bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
164730.bs2 | 164730bo1 | \([1, 0, 1, -28473, 2026588]\) | \(-105756712489/12476160\) | \(-301144172855040\) | \([2]\) | \(983040\) | \(1.5140\) | \(\Gamma_0(N)\)-optimal |
164730.bs1 | 164730bo2 | \([1, 0, 1, -467753, 123092156]\) | \(468898230633769/5540400\) | \(133731787287600\) | \([2]\) | \(1966080\) | \(1.8606\) |
Rank
sage: E.rank()
The elliptic curves in class 164730bo have rank \(1\).
Complex multiplication
The elliptic curves in class 164730bo do not have complex multiplication.Modular form 164730.2.a.bo
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.