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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 101150.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101150.bg1 | 101150g2 | \([1, 1, 0, -202450, 4124250]\) | \(2433138625/1387778\) | \(523399800495031250\) | \([2]\) | \(1327104\) | \(2.0897\) | |
101150.bg2 | 101150g1 | \([1, 1, 0, -130200, -18056500]\) | \(647214625/3332\) | \(1256662186062500\) | \([2]\) | \(663552\) | \(1.7431\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101150.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 101150.bg do not have complex multiplication.Modular form 101150.2.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.