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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 259210cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259210.cg2 | 259210cg1 | \([1, 1, 1, -236400060, 1340659838237]\) | \(83890194895342081/3958384640000\) | \(68940312694784298199040000\) | \([2]\) | \(113541120\) | \(3.7187\) | \(\Gamma_0(N)\)-optimal |
259210.cg1 | 259210cg2 | \([1, 1, 1, -651136060, -4650118734563]\) | \(1753007192038126081/478174101507200\) | \(8328011317377660342537219200\) | \([2]\) | \(227082240\) | \(4.0652\) |
Rank
sage: E.rank()
The elliptic curves in class 259210cg have rank \(1\).
Complex multiplication
The elliptic curves in class 259210cg do not have complex multiplication.Modular form 259210.2.a.cg
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.