Properties

Label 9702.bk
Number of curves $2$
Conductor $9702$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bk1")
 
sage: 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)
 
\(q + q^{2} + q^{4} + q^{8} - q^{11} - 4 q^{13} + q^{16} - 4 q^{17} + O(q^{20})\)  Toggle raw display

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.