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SageMath
sage: E = EllipticCurve("m1")
sage: E.isogeny_class()
Elliptic curves in class 1666.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
1666.m1 | 1666l4 | [1, 1, 1, -5538, 107309] | [2] | 3456 | |
1666.m2 | 1666l3 | [1, 1, 1, -5048, 135925] | [2] | 1728 | |
1666.m3 | 1666l2 | [1, 1, 1, -2108, -38123] | [2] | 1152 | |
1666.m4 | 1666l1 | [1, 1, 1, -148, -491] | [2] | 576 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1666.m have rank \(0\).
Complex multiplication
The elliptic curves in class 1666.m do not have complex multiplication.Modular form 1666.2.a.m
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.