Show commands:
SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 9702.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.bk1 | 9702bu2 | \([1, -1, 1, -650390, -201724491]\) | \(121681065322255375/12702096\) | \(3176120998512\) | \([2]\) | \(65536\) | \(1.8278\) | |
9702.bk2 | 9702bu1 | \([1, -1, 1, -40550, -3160587]\) | \(-29489309167375/303595776\) | \(-75913213001472\) | \([2]\) | \(32768\) | \(1.4812\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 9702.bk do not have complex multiplication.Modular form 9702.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.