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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 27930bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27930.by2 | 27930bo1 | \([1, 0, 1, -3848, 321878]\) | \(-53540005609/350208000\) | \(-41201620992000\) | \([2]\) | \(120960\) | \(1.2959\) | \(\Gamma_0(N)\)-optimal |
27930.by1 | 27930bo2 | \([1, 0, 1, -97928, 11762006]\) | \(882774443450089/2166000000\) | \(254827734000000\) | \([2]\) | \(241920\) | \(1.6425\) |
Rank
sage: E.rank()
The elliptic curves in class 27930bo have rank \(0\).
Complex multiplication
The elliptic curves in class 27930bo do not have complex multiplication.Modular form 27930.2.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.