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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 274890cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
274890.cx2 | 274890cx1 | \([1, 0, 1, 1297, -15634]\) | \(2053225511/2098140\) | \(-246844072860\) | \([2]\) | \(368640\) | \(0.87284\) | \(\Gamma_0(N)\)-optimal |
274890.cx1 | 274890cx2 | \([1, 0, 1, -7033, -145582]\) | \(326940373369/112003650\) | \(13177117418850\) | \([2]\) | \(737280\) | \(1.2194\) |
Rank
sage: E.rank()
The elliptic curves in class 274890cx have rank \(1\).
Complex multiplication
The elliptic curves in class 274890cx do not have complex multiplication.Modular form 274890.2.a.cx
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.