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SageMath
sage: E = EllipticCurve("fg1")
sage: E.isogeny_class()
Elliptic curves in class 76230.fg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
76230.fg1 | 76230fe4 | [1, -1, 1, -291512, -60504551] | [2] | 655360 | |
76230.fg2 | 76230fe3 | [1, -1, 1, -95492, 10637641] | [2] | 655360 | |
76230.fg3 | 76230fe2 | [1, -1, 1, -19262, -827351] | [2, 2] | 327680 | |
76230.fg4 | 76230fe1 | [1, -1, 1, 2518, -78119] | [2] | 163840 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76230.fg have rank \(0\).
Complex multiplication
The elliptic curves in class 76230.fg do not have complex multiplication.Modular form 76230.2.a.fg
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.