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Properties

Label 160446a
Number of curves $2$
Conductor $160446$
CM no
Rank $0$
Graph

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

Elliptic curves in class 160446a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.bg1 160446a1 \([1, 0, 0, -4774360, -3439036864]\) \(6793805286030262681/1048227429629952\) \(1856998833462667395072\) \([2]\) \(18063360\) \(2.8045\) \(\Gamma_0(N)\)-optimal
160446.bg2 160446a2 \([1, 0, 0, 8313000, -18973733184]\) \(35862531227445945959/108547797844556928\) \(-192299045297301115924608\) \([2]\) \(36126720\) \(3.1511\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 160446.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 4 q^{5} + q^{6} + 2 q^{7} + q^{8} + q^{9} - 4 q^{10} + q^{12} + q^{13} + 2 q^{14} - 4 q^{15} + q^{16} + q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.