Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.l1 4560c3 \([0, -1, 0, -32840, 2301600]\) \(3825131988299044/961875\) \(984960000\) \([4]\) \(10240\) \(1.1008\)  
4560.l2 4560c2 \([0, -1, 0, -2060, 36192]\) \(3778298043856/59213025\) \(15158534400\) \([2, 2]\) \(5120\) \(0.75427\)  
4560.l3 4560c1 \([0, -1, 0, -255, -630]\) \(115060504576/52780005\) \(844480080\) \([2]\) \(2560\) \(0.40769\) \(\Gamma_0(N)\)-optimal
4560.l4 4560c4 \([0, -1, 0, -160, 98512]\) \(-445138564/4089438495\) \(-4187585018880\) \([2]\) \(10240\) \(1.1008\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 4 q^{7} + q^{9} + 4 q^{11} + 2 q^{13} - q^{15} - 6 q^{17} - q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.