Properties

Label 4560.w
Number of curves $4$
Conductor $4560$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.w1 4560bd4 \([0, 1, 0, -96120, 11438100]\) \(23977812996389881/146611125\) \(600519168000\) \([4]\) \(18432\) \(1.4473\)  
4560.w2 4560bd3 \([0, 1, 0, -19800, -875052]\) \(209595169258201/41748046875\) \(171000000000000\) \([2]\) \(18432\) \(1.4473\)  
4560.w3 4560bd2 \([0, 1, 0, -6120, 170100]\) \(6189976379881/456890625\) \(1871424000000\) \([2, 2]\) \(9216\) \(1.1007\)  
4560.w4 4560bd1 \([0, 1, 0, 360, 11988]\) \(1256216039/15582375\) \(-63825408000\) \([2]\) \(4608\) \(0.75414\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.w

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