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SageMath
E = EllipticCurve("qx1")
E.isogeny_class()
Elliptic curves in class 418950qx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.qx2 | 418950qx1 | \([1, -1, 1, -680105, -76414103]\) | \(961504803/486400\) | \(17599208029200000000\) | \([2]\) | \(13271040\) | \(2.3854\) | \(\Gamma_0(N)\)-optimal* |
418950.qx1 | 418950qx2 | \([1, -1, 1, -5972105, 5564857897]\) | \(651038076963/7220000\) | \(261238244183437500000\) | \([2]\) | \(26542080\) | \(2.7320\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950qx have rank \(0\).
Complex multiplication
The elliptic curves in class 418950qx do not have complex multiplication.Modular form 418950.2.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 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.