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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 297825.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
297825.bk1 | 297825bk2 | \([0, 1, 1, -271321583, 1720092466994]\) | \(-3004935183806464000/2037123\) | \(-1497472597505671875\) | \([]\) | \(27993600\) | \(3.2371\) | |
297825.bk2 | 297825bk1 | \([0, 1, 1, -3279083, 2462724869]\) | \(-5304438784000/497763387\) | \(-365901829233733546875\) | \([]\) | \(9331200\) | \(2.6878\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 297825.bk have rank \(2\).
Complex multiplication
The elliptic curves in class 297825.bk do not have complex multiplication.Modular form 297825.2.a.bk
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.