Properties

Label 169050.hu
Number of curves $2$
Conductor $169050$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 169050.hu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.hu1 169050bg1 \([1, 0, 0, -28813, -1040383]\) \(1439069689/579600\) \(1065458756250000\) \([2]\) \(884736\) \(1.5815\) \(\Gamma_0(N)\)-optimal
169050.hu2 169050bg2 \([1, 0, 0, 93687, -7532883]\) \(49471280711/41992020\) \(-77192486890312500\) \([2]\) \(1769472\) \(1.9281\)  

Rank

sage: E.rank()
 

The elliptic curves in class 169050.hu have rank \(1\).

Complex multiplication

The elliptic curves in class 169050.hu do not have complex multiplication.

Modular form 169050.2.a.hu

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 2q^{11} + q^{12} + 4q^{13} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20})\)  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 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.