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Properties

Label 169050du
Number of curves $2$
Conductor $169050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("du1")
 
E.isogeny_class()
 

Elliptic curves in class 169050du

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.fx2 169050du1 \([1, 1, 1, 408512, -232082719]\) \(4101378352343/15049939968\) \(-27665787301488000000\) \([2]\) \(5898240\) \(2.4134\) \(\Gamma_0(N)\)-optimal
169050.fx1 169050du2 \([1, 1, 1, -4099488, -2792626719]\) \(4144806984356137/568114785504\) \(1044345881246251500000\) \([2]\) \(11796480\) \(2.7600\)  

Rank

sage: E.rank()
 

The elliptic curves in class 169050du have rank \(0\).

Complex multiplication

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

Modular form 169050.2.a.du

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