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SageMath
E = EllipticCurve("qx1")
E.isogeny_class()
Elliptic curves in class 487872.qx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.qx1 | 487872qx2 | \([0, 0, 0, -2888028, 1618602480]\) | \(4662947952/717409\) | \(409858704878021296128\) | \([2]\) | \(22118400\) | \(2.6787\) | \(\Gamma_0(N)\)-optimal* |
487872.qx2 | 487872qx1 | \([0, 0, 0, 313632, 139435560]\) | \(95551488/290521\) | \(-10373489947842481152\) | \([2]\) | \(11059200\) | \(2.3321\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 487872.qx have rank \(1\).
Complex multiplication
The elliptic curves in class 487872.qx do not have complex multiplication.Modular form 487872.2.a.qx
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.