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SageMath
sage: E = EllipticCurve("46410.be1")
sage: E.isogeny_class()
Elliptic curves in class 46410.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
46410.be1 | 46410be8 | [1, 0, 1, -7806648, 1811198446] | [2] | 3649536 | |
46410.be2 | 46410be5 | [1, 0, 1, -5949723, 5585394256] | [6] | 1216512 | |
46410.be3 | 46410be6 | [1, 0, 1, -4730848, -3936856594] | [2, 2] | 1824768 | |
46410.be4 | 46410be3 | [1, 0, 1, -4722848, -3950910994] | [2] | 912384 | |
46410.be5 | 46410be7 | [1, 0, 1, -1783048, -8785398034] | [2] | 3649536 | |
46410.be6 | 46410be2 | [1, 0, 1, -375973, 85217756] | [2, 6] | 608256 | |
46410.be7 | 46410be1 | [1, 0, 1, -63473, -4407244] | [6] | 304128 | \(\Gamma_0(N)\)-optimal |
46410.be8 | 46410be4 | [1, 0, 1, 197777, 322291256] | [6] | 1216512 |
Rank
sage: E.rank()
The elliptic curves in class 46410.be have rank \(1\).
Modular form 46410.2.a.be
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 4 & 6 & 12 & 12 \\ 3 & 1 & 6 & 12 & 12 & 2 & 4 & 4 \\ 2 & 6 & 1 & 2 & 2 & 3 & 6 & 6 \\ 4 & 12 & 2 & 1 & 4 & 6 & 3 & 12 \\ 4 & 12 & 2 & 4 & 1 & 6 & 12 & 3 \\ 6 & 2 & 3 & 6 & 6 & 1 & 2 & 2 \\ 12 & 4 & 6 & 3 & 12 & 2 & 1 & 4 \\ 12 & 4 & 6 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.