Properties

Label 2880.k
Number of curves $4$
Conductor $2880$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2880.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.k1 2880c4 \([0, 0, 0, -73548, -7677072]\) \(8527173507/200\) \(1031956070400\) \([2]\) \(9216\) \(1.4172\)  
2880.k2 2880c3 \([0, 0, 0, -4428, -129168]\) \(-1860867/320\) \(-1651129712640\) \([2]\) \(4608\) \(1.0707\)  
2880.k3 2880c2 \([0, 0, 0, -1548, 6128]\) \(57960603/31250\) \(221184000000\) \([2]\) \(3072\) \(0.86793\)  
2880.k4 2880c1 \([0, 0, 0, 372, 752]\) \(804357/500\) \(-3538944000\) \([2]\) \(1536\) \(0.52136\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2880.k have rank \(1\).

Complex multiplication

The elliptic curves in class 2880.k do not have complex multiplication.

Modular form 2880.2.a.k

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.