Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("4560.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4560.s3 4560x1 [0, 1, 0, -496, -4396] [2] 1536 \(\Gamma_0(N)\)-optimal
4560.s2 4560x2 [0, 1, 0, -816, 1620] [2, 2] 3072  
4560.s1 4560x3 [0, 1, 0, -9936, 377364] [2] 6144  
4560.s4 4560x4 [0, 1, 0, 3184, 16020] [4] 6144  

Rank

sage: E.rank()
 

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

Modular form 4560.2.a.s

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

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 Cremona 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 Cremona labels.