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Properties

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

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Show commands: SageMath
E = EllipticCurve("hg1")
 
E.isogeny_class()
 

Elliptic curves in class 169050hg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.l2 169050hg1 \([1, 1, 0, -1338950, -596803500]\) \(5776556465785/1073088\) \(49315519575000000\) \([]\) \(3265920\) \(2.2053\) \(\Gamma_0(N)\)-optimal
169050.l1 169050hg2 \([1, 1, 0, -3268325, 1454122125]\) \(84013940106985/28705554432\) \(1319210848972800000000\) \([]\) \(9797760\) \(2.7546\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 169050.2.a.hg

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.