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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 63426.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63426.bg1 | 63426bh4 | \([1, 0, 0, -338292, 75704910]\) | \(4824238966273/66\) | \(58575242946\) | \([2]\) | \(491520\) | \(1.6220\) | |
63426.bg2 | 63426bh2 | \([1, 0, 0, -21162, 1179360]\) | \(1180932193/4356\) | \(3865966034436\) | \([2, 2]\) | \(245760\) | \(1.2755\) | |
63426.bg3 | 63426bh3 | \([1, 0, 0, -11552, 2257602]\) | \(-192100033/2371842\) | \(-2105018505750402\) | \([2]\) | \(491520\) | \(1.6220\) | |
63426.bg4 | 63426bh1 | \([1, 0, 0, -1942, -748]\) | \(912673/528\) | \(468601943568\) | \([2]\) | \(122880\) | \(0.92889\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63426.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 63426.bg do not have complex multiplication.Modular form 63426.2.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.