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SageMath
sage: E = EllipticCurve("t1")
sage: E.isogeny_class()
Elliptic curves in class 3920.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
3920.t1 | 3920ba3 | [0, 0, 0, -209867, -37003526] | [2] | 18432 | |
3920.t2 | 3920ba4 | [0, 0, 0, -68747, 6483386] | [4] | 18432 | |
3920.t3 | 3920ba2 | [0, 0, 0, -13867, -508326] | [2, 2] | 9216 | |
3920.t4 | 3920ba1 | [0, 0, 0, 1813, -47334] | [2] | 4608 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3920.t have rank \(0\).
Complex multiplication
The elliptic curves in class 3920.t do not have complex multiplication.Modular form 3920.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.