Properties

Label 6080.m
Number of curves $2$
Conductor $6080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 6080.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6080.m1 6080g2 \([0, 0, 0, -412, -3216]\) \(472058064/475\) \(7782400\) \([2]\) \(1536\) \(0.24141\)  
6080.m2 6080g1 \([0, 0, 0, -32, -24]\) \(3538944/1805\) \(1848320\) \([2]\) \(768\) \(-0.10516\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6080.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2 q^{7} - 3 q^{9} + 4 q^{11} + 4 q^{13} + 6 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.