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Properties

Label 160446q
Number of curves $2$
Conductor $160446$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 160446q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.bw1 160446q1 \([1, 0, 0, -11316, 329088]\) \(90458382169/25788048\) \(45685100102928\) \([2]\) \(768000\) \(1.3277\) \(\Gamma_0(N)\)-optimal
160446.bw2 160446q2 \([1, 0, 0, 29824, 2180388]\) \(1656015369191/2114999172\) \(-3746850048147492\) \([2]\) \(1536000\) \(1.6743\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 160446.2.a.q

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