Properties

Label 346560.ko
Number of curves $2$
Conductor $346560$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ko1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 346560.ko

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.ko1 346560ko2 \([0, 1, 0, -233345, -43463457]\) \(781484460931/900\) \(1618241126400\) \([2]\) \(1474560\) \(1.6267\)  
346560.ko2 346560ko1 \([0, 1, 0, -14465, -694305]\) \(-186169411/6480\) \(-11651336110080\) \([2]\) \(737280\) \(1.2801\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 346560.ko have rank \(1\).

Complex multiplication

The elliptic curves in class 346560.ko do not have complex multiplication.

Modular form 346560.2.a.ko

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{13} + q^{15} - 6q^{17} + O(q^{20})\)  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.