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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 22050cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.r2 | 22050cq1 | \([1, -1, 0, -492, -18334]\) | \(-189/2\) | \(-139535156250\) | \([]\) | \(23040\) | \(0.82058\) | \(\Gamma_0(N)\)-optimal |
22050.r1 | 22050cq2 | \([1, -1, 0, -1536117, 733183541]\) | \(-5745702166029/8192\) | \(-571536000000000\) | \([]\) | \(299520\) | \(2.1031\) |
Rank
sage: E.rank()
The elliptic curves in class 22050cq have rank \(0\).
Complex multiplication
The elliptic curves in class 22050cq do not have complex multiplication.Modular form 22050.2.a.cq
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.