Properties

Label 4560.f
Number of curves $2$
Conductor $4560$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.f1 4560p2 \([0, -1, 0, -116, -420]\) \(680136784/38475\) \(9849600\) \([2]\) \(768\) \(0.096521\)  
4560.f2 4560p1 \([0, -1, 0, -21, 36]\) \(67108864/16245\) \(259920\) \([2]\) \(384\) \(-0.25005\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4560.f have rank \(1\).

Complex multiplication

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

Modular form 4560.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.