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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 328510.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 328510.bx1 | 328510bx4 | \([1, 1, 1, -5295336, 4687877489]\) | \(349046010201856969/7245875000\) | \(340888572990875000\) | \([2]\) | \(12317184\) | \(2.4829\) | |
| 328510.bx2 | 328510bx3 | \([1, 1, 1, -342416, 67793713]\) | \(94376601570889/12235496000\) | \(575629688791976000\) | \([2]\) | \(6158592\) | \(2.1364\) | |
| 328510.bx3 | 328510bx2 | \([1, 1, 1, -109571, -3348557]\) | \(3092354182009/1689383150\) | \(79478518638305150\) | \([2]\) | \(4105728\) | \(1.9336\) | |
| 328510.bx4 | 328510bx1 | \([1, 1, 1, -84301, -9443681]\) | \(1408317602329/2153060\) | \(101292604545860\) | \([2]\) | \(2052864\) | \(1.5871\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 328510.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 328510.bx do not have complex multiplication.Modular form 328510.2.a.bx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
