Properties

Label 257600.dk
Number of curves $2$
Conductor $257600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 257600.dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.dk1 257600dk1 \([0, 0, 0, -4700, 114000]\) \(44851536/4025\) \(1030400000000\) \([2]\) \(245760\) \(1.0448\) \(\Gamma_0(N)\)-optimal
257600.dk2 257600dk2 \([0, 0, 0, 5300, 534000]\) \(16078716/129605\) \(-132715520000000\) \([2]\) \(491520\) \(1.3914\)  

Rank

sage: E.rank()
 

The elliptic curves in class 257600.dk have rank \(1\).

Complex multiplication

The elliptic curves in class 257600.dk do not have complex multiplication.

Modular form 257600.2.a.dk

sage: E.q_eigenform(10)
 
\(q + q^{7} - 3 q^{9} - 2 q^{11} - 4 q^{13} - 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.