Properties

Label 160080.k
Number of curves $2$
Conductor $160080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 160080.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160080.k1 160080bw1 \([0, -1, 0, -443576, -109601424]\) \(2356507705137010489/93358656000000\) \(382397054976000000\) \([2]\) \(1935360\) \(2.1405\) \(\Gamma_0(N)\)-optimal
160080.k2 160080bw2 \([0, -1, 0, 196424, -400417424]\) \(204618645563149511/17023122363528000\) \(-69726709201010688000\) \([2]\) \(3870720\) \(2.4871\)  

Rank

sage: E.rank()
 

The elliptic curves in class 160080.k have rank \(0\).

Complex multiplication

The elliptic curves in class 160080.k do not have complex multiplication.

Modular form 160080.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 2 q^{11} - 6 q^{13} + q^{15} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.