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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 4704.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4704.bg1 | 4704bg2 | \([0, 1, 0, -73761, 6046767]\) | \(92100460096/20253807\) | \(9760113212387328\) | \([2]\) | \(46080\) | \(1.7816\) | |
4704.bg2 | 4704bg1 | \([0, 1, 0, 10274, 584492]\) | \(15926924096/28588707\) | \(-215259698549952\) | \([2]\) | \(23040\) | \(1.4350\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4704.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 4704.bg do not have complex multiplication.Modular form 4704.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.