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SageMath
E = EllipticCurve("ii1")
E.isogeny_class()
Elliptic curves in class 227850ii
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227850.d2 | 227850ii1 | \([1, 1, 0, -232775, -14260875]\) | \(2212245127/1142784\) | \(720554006592000000\) | \([2]\) | \(5160960\) | \(2.1186\) | \(\Gamma_0(N)\)-optimal |
227850.d1 | 227850ii2 | \([1, 1, 0, -2976775, -1976220875]\) | \(4626574746247/4981824\) | \(3141165122487000000\) | \([2]\) | \(10321920\) | \(2.4652\) |
Rank
sage: E.rank()
The elliptic curves in class 227850ii have rank \(0\).
Complex multiplication
The elliptic curves in class 227850ii do not have complex multiplication.Modular form 227850.2.a.ii
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.