Properties

Label 154560.by
Number of curves $6$
Conductor $154560$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("by1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 154560.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.by1 154560hp6 \([0, -1, 0, -5688641, -5220392895]\) \(155324313723954725282/13018359375\) \(1706342400000000\) \([2]\) \(3670016\) \(2.3652\)  
154560.by2 154560hp3 \([0, -1, 0, -489601, 131883265]\) \(198048499826486404/242568272835\) \(15896954328514560\) \([2]\) \(1835008\) \(2.0187\)  
154560.by3 154560hp4 \([0, -1, 0, -356321, -81102879]\) \(76343005935514084/694180580625\) \(45493818531840000\) \([2, 2]\) \(1835008\) \(2.0187\)  
154560.by4 154560hp5 \([0, -1, 0, -104321, -193847679]\) \(-957928673903042/123339801817575\) \(-16166394503833190400\) \([2]\) \(3670016\) \(2.3652\)  
154560.by5 154560hp2 \([0, -1, 0, -38801, 880785]\) \(394315384276816/208332909225\) \(3413326384742400\) \([2, 2]\) \(917504\) \(1.6721\)  
154560.by6 154560hp1 \([0, -1, 0, 9219, 102861]\) \(84611246065664/53699121315\) \(-54987900226560\) \([2]\) \(458752\) \(1.3255\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 154560.by have rank \(0\).

Complex multiplication

The elliptic curves in class 154560.by do not have complex multiplication.

Modular form 154560.2.a.by

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.