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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 333795.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333795.bg1 | 333795bg2 | \([0, -1, 1, -243145, -46068444]\) | \(-65860951343104/3493875\) | \(-84333648889875\) | \([]\) | \(2177280\) | \(1.7400\) | |
333795.bg2 | 333795bg1 | \([0, -1, 1, -385, -168597]\) | \(-262144/509355\) | \(-12294591457995\) | \([]\) | \(725760\) | \(1.1907\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333795.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 333795.bg do not have complex multiplication.Modular form 333795.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.