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SageMath
sage: E = EllipticCurve("h1")
sage: E.isogeny_class()
Elliptic curves in class 1050.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 1050.h1 | 1050g5 | [1, 0, 1, -420001, -104801602] | [2] | 6144 | |
| 1050.h2 | 1050g3 | [1, 0, 1, -26251, -1639102] | [2, 2] | 3072 | |
| 1050.h3 | 1050g6 | [1, 0, 1, -24501, -1866602] | [2] | 6144 | |
| 1050.h4 | 1050g4 | [1, 0, 1, -9251, 322898] | [2] | 3072 | |
| 1050.h5 | 1050g2 | [1, 0, 1, -1751, -22102] | [2, 2] | 1536 | |
| 1050.h6 | 1050g1 | [1, 0, 1, 249, -2102] | [2] | 768 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1050.h have rank \(0\).
Complex multiplication
The elliptic curves in class 1050.h do not have complex multiplication.Modular form 1050.2.a.h
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.
