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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 20160.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20160.bs1 | 20160bq3 | \([0, 0, 0, -4728, 130898]\) | \(-250523582464/13671875\) | \(-637875000000\) | \([]\) | \(25920\) | \(1.0233\) | |
20160.bs2 | 20160bq1 | \([0, 0, 0, -48, -142]\) | \(-262144/35\) | \(-1632960\) | \([]\) | \(2880\) | \(-0.075270\) | \(\Gamma_0(N)\)-optimal |
20160.bs3 | 20160bq2 | \([0, 0, 0, 312, 362]\) | \(71991296/42875\) | \(-2000376000\) | \([]\) | \(8640\) | \(0.47404\) |
Rank
sage: E.rank()
The elliptic curves in class 20160.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 20160.bs do not have complex multiplication.Modular form 20160.2.a.bs
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.