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SageMath
sage: E = EllipticCurve("q1")
sage: E.isogeny_class()
Elliptic curves in class 1050.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
1050.q1 | 1050p3 | [1, 0, 0, -9338, 346542] | [2] | 1536 | |
1050.q2 | 1050p2 | [1, 0, 0, -588, 5292] | [2, 2] | 768 | |
1050.q3 | 1050p1 | [1, 0, 0, -88, -208] | [2] | 384 | \(\Gamma_0(N)\)-optimal |
1050.q4 | 1050p4 | [1, 0, 0, 162, 18042] | [2] | 1536 |
Rank
sage: E.rank()
The elliptic curves in class 1050.q have rank \(0\).
Complex multiplication
The elliptic curves in class 1050.q do not have complex multiplication.Modular form 1050.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.