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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 22218c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22218.d2 | 22218c1 | \([1, 1, 0, -7799851, -10260900611]\) | \(-354499561600764553/101902222098432\) | \(-15085186039416826626048\) | \([2]\) | \(2230272\) | \(2.9707\) | \(\Gamma_0(N)\)-optimal |
22218.d1 | 22218c2 | \([1, 1, 0, -132389931, -586340512515]\) | \(1733490909744055732873/99355964553216\) | \(14708248540087818369024\) | \([2]\) | \(4460544\) | \(3.3172\) |
Rank
sage: E.rank()
The elliptic curves in class 22218c have rank \(0\).
Complex multiplication
The elliptic curves in class 22218c do not have complex multiplication.Modular form 22218.2.a.c
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.