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SageMath
sage: E = EllipticCurve("bg1")
sage: E.isogeny_class()
Elliptic curves in class 151725.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
151725.bg1 | 151725t4 | [1, 0, 0, -812963, -282180708] | [2] | 1966080 | |
151725.bg2 | 151725t2 | [1, 0, 0, -54338, -3765333] | [2, 2] | 983040 | |
151725.bg3 | 151725t1 | [1, 0, 0, -18213, 894792] | [2] | 491520 | \(\Gamma_0(N)\)-optimal |
151725.bg4 | 151725t3 | [1, 0, 0, 126287, -23453458] | [2] | 1966080 |
Rank
sage: E.rank()
The elliptic curves in class 151725.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 151725.bg do not have complex multiplication.Modular form 151725.2.a.bg
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.