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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 364650cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.cx1 | 364650cx1 | \([1, 0, 1, -2108451, -1178503202]\) | \(66342819962001390625/4812668669952\) | \(75197947968000000\) | \([2]\) | \(8515584\) | \(2.2894\) | \(\Gamma_0(N)\)-optimal |
364650.cx2 | 364650cx2 | \([1, 0, 1, -1972451, -1337079202]\) | \(-54315282059491182625/17983956399469632\) | \(-280999318741713000000\) | \([2]\) | \(17031168\) | \(2.6360\) |
Rank
sage: E.rank()
The elliptic curves in class 364650cx have rank \(1\).
Complex multiplication
The elliptic curves in class 364650cx do not have complex multiplication.Modular form 364650.2.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.