Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 160446v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.z1 160446v1 \([1, 1, 1, -365483, 77202137]\) \(3047678972871625/304559880768\) \(539546406933238848\) \([2]\) \(2580480\) \(2.1388\) \(\Gamma_0(N)\)-optimal
160446.z2 160446v2 \([1, 1, 1, 452477, 374612393]\) \(5783051584712375/37533175779528\) \(-66492310417156403208\) \([2]\) \(5160960\) \(2.4854\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 160446.2.a.v

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