Properties

Label 160446.bo
Number of curves $4$
Conductor $160446$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 160446.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.bo1 160446i3 \([1, 0, 0, -398721683, 3063902480673]\) \(3957101249824708884951625/772310238681366528\) \(1368194698748600367710208\) \([2]\) \(54743040\) \(3.6310\)  
160446.bo2 160446i4 \([1, 0, 0, -356594323, 3736617441569]\) \(-2830680648734534916567625/1766676274677722124288\) \(-3129774787844340084225773568\) \([2]\) \(109486080\) \(3.9776\)  
160446.bo3 160446i1 \([1, 0, 0, -12139388, -10542660336]\) \(111675519439697265625/37528570137307392\) \(66484151241018420678912\) \([2]\) \(18247680\) \(3.0817\) \(\Gamma_0(N)\)-optimal
160446.bo4 160446i2 \([1, 0, 0, 35418452, -72852942304]\) \(2773679829880629422375/2899504554614368272\) \(-5136649188277184870312592\) \([2]\) \(36495360\) \(3.4283\)  

Rank

sage: E.rank()
 

The elliptic curves in class 160446.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 160446.bo do not have complex multiplication.

Modular form 160446.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 4 q^{7} + q^{8} + q^{9} + q^{12} - q^{13} + 4 q^{14} + q^{16} - q^{17} + q^{18} - 2 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.