Properties

Label 32760.l
Number of curves $4$
Conductor $32760$
CM no
Rank $0$
Graph

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

Elliptic curves in class 32760.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32760.l1 32760bh4 \([0, 0, 0, -625323, 190326022]\) \(18112543427820242/316031625\) \(471832687872000\) \([2]\) \(294912\) \(1.9440\)  
32760.l2 32760bh2 \([0, 0, 0, -40323, 2775022]\) \(9713030100484/1164515625\) \(869306256000000\) \([2, 2]\) \(147456\) \(1.5974\)  
32760.l3 32760bh1 \([0, 0, 0, -9903, -333902]\) \(575514878416/74972625\) \(13991691168000\) \([2]\) \(73728\) \(1.2508\) \(\Gamma_0(N)\)-optimal
32760.l4 32760bh3 \([0, 0, 0, 57957, 14195158]\) \(14420619677518/66650390625\) \(-99508500000000000\) \([2]\) \(294912\) \(1.9440\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32760.l have rank \(0\).

Complex multiplication

The elliptic curves in class 32760.l do not have complex multiplication.

Modular form 32760.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.