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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 274890.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
274890.k1 | 274890k2 | \([1, 1, 0, -331617423, -2324275211817]\) | \(99943228448001537681727/11290335851990250\) | \(455605775869224716331750\) | \([2]\) | \(101154816\) | \(3.5676\) | |
274890.k2 | 274890k1 | \([1, 1, 0, -19058673, -42408801567]\) | \(-18972272930584701727/8267129411062500\) | \(-333608491272157577437500\) | \([2]\) | \(50577408\) | \(3.2210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 274890.k have rank \(0\).
Complex multiplication
The elliptic curves in class 274890.k do not have complex multiplication.Modular form 274890.2.a.k
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.