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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 142912bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142912.g2 | 142912bg1 | \([0, 1, 0, -3393, -77921]\) | \(-65936114500/712327\) | \(-46683062272\) | \([2]\) | \(126976\) | \(0.86318\) | \(\Gamma_0(N)\)-optimal |
142912.g1 | 142912bg2 | \([0, 1, 0, -54433, -4906305]\) | \(136084473031250/15631\) | \(2048786432\) | \([2]\) | \(253952\) | \(1.2098\) |
Rank
sage: E.rank()
The elliptic curves in class 142912bg have rank \(0\).
Complex multiplication
The elliptic curves in class 142912bg do not have complex multiplication.Modular form 142912.2.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 Cremona 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 Cremona labels.