Properties

Label 199962.bk
Number of curves $3$
Conductor $199962$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 199962.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
199962.bk1 199962k3 \([1, -1, 1, -5057075, 4378472173]\) \(-545407363875/14\) \(-367137590801562\) \([]\) \(3528360\) \(2.3109\)  
199962.bk2 199962k2 \([1, -1, 1, -58025, 6902929]\) \(-7414875/2744\) \(-7995440866345128\) \([]\) \(1176120\) \(1.7616\)  
199962.bk3 199962k1 \([1, -1, 1, 5455, -96799]\) \(4492125/3584\) \(-14325136906752\) \([]\) \(392040\) \(1.2123\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 199962.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 199962.bk do not have complex multiplication.

Modular form 199962.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} + 5 q^{13} - q^{14} + q^{16} - 3 q^{17} - 2 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.