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SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 88200gx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88200.bg2 | 88200gx1 | \([0, 0, 0, 437325, 121850750]\) | \(19652/25\) | \(-11767111801200000000\) | \([2]\) | \(1548288\) | \(2.3453\) | \(\Gamma_0(N)\)-optimal |
88200.bg1 | 88200gx2 | \([0, 0, 0, -2649675, 1180691750]\) | \(2185454/625\) | \(588355590060000000000\) | \([2]\) | \(3096576\) | \(2.6919\) |
Rank
sage: E.rank()
The elliptic curves in class 88200gx have rank \(0\).
Complex multiplication
The elliptic curves in class 88200gx do not have complex multiplication.Modular form 88200.2.a.gx
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.