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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 9702.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.bd1 | 9702ce1 | \([1, -1, 1, -104, 627]\) | \(-3451273/2376\) | \(-84873096\) | \([]\) | \(3456\) | \(0.22171\) | \(\Gamma_0(N)\)-optimal |
| 9702.bd2 | 9702ce2 | \([1, -1, 1, 841, -9201]\) | \(1843623047/2044416\) | \(-73028583936\) | \([]\) | \(10368\) | \(0.77102\) |
Rank
sage: E.rank()
The elliptic curves in class 9702.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 9702.bd do not have complex multiplication.Modular form 9702.2.a.bd
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.
