Properties

Label 115920.dk
Number of curves $2$
Conductor $115920$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("dk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dk1 115920ek1 \([0, 0, 0, -16169187, 25025360866]\) \(156567200830221067489/16905000000\) \(50478059520000000\) \([2]\) \(3354624\) \(2.6319\) \(\Gamma_0(N)\)-optimal
115920.dk2 115920ek2 \([0, 0, 0, -16128867, 25156376674]\) \(-155398856216042825569/1627294921875000\) \(-4859076600000000000000\) \([2]\) \(6709248\) \(2.9785\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.dk have rank \(1\).

Complex multiplication

The elliptic curves in class 115920.dk do not have complex multiplication.

Modular form 115920.2.a.dk

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 6 q^{13} - 4 q^{17} - 4 q^{19} + O(q^{20})\)  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.