Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 160446.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.d1 160446bq1 \([1, 1, 0, -10204900, 12542579152]\) \(66342819962001390625/4812668669952\) \(8525936121608835072\) \([2]\) \(7096320\) \(2.6836\) \(\Gamma_0(N)\)-optimal
160446.d2 160446bq2 \([1, 1, 0, -9546660, 14231491344]\) \(-54315282059491182625/17983956399469632\) \(-31859675783000820735552\) \([2]\) \(14192640\) \(3.0302\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 160446.2.a.d

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