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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 9702.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.bp1 | 9702cc2 | \([1, -1, 1, -199435865, 1068707030073]\) | \(10228636028672744397625/167006381634183168\) | \(14323489535009531322851328\) | \([2]\) | \(3194880\) | \(3.6262\) | |
| 9702.bp2 | 9702cc1 | \([1, -1, 1, -738905, 46848304185]\) | \(-520203426765625/11054534935707648\) | \(-948104580894629358993408\) | \([2]\) | \(1597440\) | \(3.2796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 9702.bp do not have complex multiplication.Modular form 9702.2.a.bp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
