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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 177450io
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177450.bb1 | 177450io1 | \([1, 1, 0, -720450, 233806500]\) | \(4386781853/27216\) | \(256575065906250000\) | \([2]\) | \(3686400\) | \(2.1785\) | \(\Gamma_0(N)\)-optimal |
177450.bb2 | 177450io2 | \([1, 1, 0, -297950, 506319000]\) | \(-310288733/11573604\) | \(-109108546776632812500\) | \([2]\) | \(7372800\) | \(2.5251\) |
Rank
sage: E.rank()
The elliptic curves in class 177450io have rank \(0\).
Complex multiplication
The elliptic curves in class 177450io do not have complex multiplication.Modular form 177450.2.a.io
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.