Properties

Label 73920.dw
Number of curves $4$
Conductor $73920$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920.dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.dw1 73920bu4 \([0, -1, 0, -198385, 17998225]\) \(52702650535889104/22020583921875\) \(360785246976000000\) \([2]\) \(995328\) \(2.0660\)  
73920.dw2 73920bu2 \([0, -1, 0, -171025, 27280177]\) \(33766427105425744/9823275\) \(160944537600\) \([2]\) \(331776\) \(1.5167\)  
73920.dw3 73920bu1 \([0, -1, 0, -10645, 432565]\) \(-130287139815424/2250652635\) \(-2304668298240\) \([2]\) \(165888\) \(1.1701\) \(\Gamma_0(N)\)-optimal
73920.dw4 73920bu3 \([0, -1, 0, 41195, 2042197]\) \(7549996227362816/6152409907875\) \(-6300067745664000\) \([2]\) \(497664\) \(1.7194\)  

Rank

sage: E.rank()
 

The elliptic curves in class 73920.dw have rank \(2\).

Complex multiplication

The elliptic curves in class 73920.dw do not have complex multiplication.

Modular form 73920.2.a.dw

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} + q^{11} - 2q^{13} - q^{15} - 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.