Properties

Label 6080.k
Number of curves $4$
Conductor $6080$
CM no
Rank $0$
Graph

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

Elliptic curves in class 6080.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6080.k1 6080c4 \([0, 0, 0, -8108, 281008]\) \(899466517764/95\) \(6225920\) \([2]\) \(4096\) \(0.73189\)  
6080.k2 6080c3 \([0, 0, 0, -908, -3472]\) \(1263284964/651605\) \(42703585280\) \([2]\) \(4096\) \(0.73189\)  
6080.k3 6080c2 \([0, 0, 0, -508, 4368]\) \(884901456/9025\) \(147865600\) \([2, 2]\) \(2048\) \(0.38532\)  
6080.k4 6080c1 \([0, 0, 0, -8, 168]\) \(-55296/11875\) \(-12160000\) \([2]\) \(1024\) \(0.038746\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6080.k have rank \(0\).

Complex multiplication

The elliptic curves in class 6080.k do not have complex multiplication.

Modular form 6080.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{5} - 3 q^{9} + 4 q^{11} + 6 q^{13} - 6 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.