Properties

Label 160446.a
Number of curves $4$
Conductor $160446$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 160446.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.a1 160446bn3 \([1, 1, 0, -303668030426, 64408869849277716]\) \(1748094148784980747354970849498497/887694600425282263291392\) \(1572605134024013471638761702912\) \([2]\) \(1134673920\) \(5.1269\)  
160446.a2 160446bn4 \([1, 1, 0, -41539825626, -1792140629348076]\) \(4474676144192042711273397261697/1806328356954994499451382272\) \(3200020870375547010442590229166592\) \([2]\) \(1134673920\) \(5.1269\)  
160446.a3 160446bn2 \([1, 1, 0, -19081915866, 994944362433300]\) \(433744050935826360922067531137/9612122270219882316693504\) \(17028460941153004936843860639744\) \([2, 2]\) \(567336960\) \(4.7804\)  
160446.a4 160446bn1 \([1, 1, 0, 108335654, 47655976651540]\) \(79374649975090937760383/553856914190911653543936\) \(-981191308760965639863948804096\) \([2]\) \(283668480\) \(4.4338\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 160446.a have rank \(1\).

Complex multiplication

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

Modular form 160446.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - q^{8} + q^{9} + 2q^{10} - q^{12} - q^{13} + 2q^{15} + q^{16} + q^{17} - q^{18} - 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.