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SageMath
sage: E = EllipticCurve("bq1")
sage: E.isogeny_class()
Elliptic curves in class 24255.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 24255.bq1 | 24255bs6 | [1, -1, 0, -1344697209, -18979168274060] | [2] | 2949120 | |
| 24255.bq2 | 24255bs4 | [1, -1, 0, -84043584, -296533682285] | [2, 2] | 1474560 | |
| 24255.bq3 | 24255bs5 | [1, -1, 0, -83626839, -299620345802] | [4] | 2949120 | |
| 24255.bq4 | 24255bs3 | [1, -1, 0, -11221254, 7632484033] | [2] | 1474560 | |
| 24255.bq5 | 24255bs2 | [1, -1, 0, -5278779, -4584056072] | [2, 2] | 737280 | |
| 24255.bq6 | 24255bs1 | [1, -1, 0, 15426, -214219265] | [2] | 368640 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24255.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 24255.bq do not have complex multiplication.Modular form 24255.2.a.bq
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
