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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 182070bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
182070.ce2 | 182070bk1 | \([1, -1, 1, -2337053, 12856812581]\) | \(-16329068153/816480000\) | \(-70585154834255238240000\) | \([2]\) | \(20054016\) | \(3.0642\) | \(\Gamma_0(N)\)-optimal |
182070.ce1 | 182070bk2 | \([1, -1, 1, -97845773, 370326849797]\) | \(1198345620520313/8268750000\) | \(714838084258950618750000\) | \([2]\) | \(40108032\) | \(3.4108\) |
Rank
sage: E.rank()
The elliptic curves in class 182070bk have rank \(1\).
Complex multiplication
The elliptic curves in class 182070bk do not have complex multiplication.Modular form 182070.2.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 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.