Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.x1 4560bc3 \([0, 1, 0, -7879680, -8516182860]\) \(13209596798923694545921/92340\) \(378224640\) \([2]\) \(92160\) \(2.1806\)  
4560.x2 4560bc4 \([0, 1, 0, -498560, -129737292]\) \(3345930611358906241/165622259047500\) \(678388773058560000\) \([4]\) \(92160\) \(2.1806\)  
4560.x3 4560bc2 \([0, 1, 0, -492480, -133188300]\) \(3225005357698077121/8526675600\) \(34925263257600\) \([2, 2]\) \(46080\) \(1.8341\)  
4560.x4 4560bc1 \([0, 1, 0, -30400, -2142412]\) \(-758575480593601/40535043840\) \(-166031539568640\) \([2]\) \(23040\) \(1.4875\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.x

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