Properties

Label 4560.k
Number of curves $4$
Conductor $4560$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4560.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.k1 4560u3 \([0, -1, 0, -48640, -4112768]\) \(3107086841064961/570\) \(2334720\) \([2]\) \(9216\) \(1.0577\)  
4560.k2 4560u4 \([0, -1, 0, -3520, -41600]\) \(1177918188481/488703750\) \(2001730560000\) \([4]\) \(9216\) \(1.0577\)  
4560.k3 4560u2 \([0, -1, 0, -3040, -63488]\) \(758800078561/324900\) \(1330790400\) \([2, 2]\) \(4608\) \(0.71109\)  
4560.k4 4560u1 \([0, -1, 0, -160, -1280]\) \(-111284641/123120\) \(-504299520\) \([2]\) \(2304\) \(0.36452\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4560.k have rank \(0\).

Complex multiplication

The elliptic curves in class 4560.k do not have complex multiplication.

Modular form 4560.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 4 q^{7} + q^{9} + 4 q^{11} - 2 q^{13} - q^{15} - 2 q^{17} + q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.