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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 222768.eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
222768.eo1 | 222768di2 | \([0, 0, 0, -79299, -3285630]\) | \(684030715731/338005577\) | \(27250539610484736\) | \([2]\) | \(1474560\) | \(1.8467\) | |
222768.eo2 | 222768di1 | \([0, 0, 0, -42579, 3346002]\) | \(105890949891/1288651\) | \(103893064224768\) | \([2]\) | \(737280\) | \(1.5002\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 222768.eo have rank \(1\).
Complex multiplication
The elliptic curves in class 222768.eo do not have complex multiplication.Modular form 222768.2.a.eo
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.