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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 9702.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.bs1 | 9702by2 | \([1, -1, 1, -119300, -15669489]\) | \(911871625/10648\) | \(2192683613035608\) | \([]\) | \(60480\) | \(1.7559\) | |
9702.bs2 | 9702by1 | \([1, -1, 1, -11255, 450825]\) | \(765625/22\) | \(4530338043462\) | \([]\) | \(20160\) | \(1.2066\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 9702.bs do not have complex multiplication.Modular form 9702.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.