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Properties

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

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Show commands: SageMath
E = EllipticCurve("jc1")
 
E.isogeny_class()
 

Elliptic curves in class 169050jc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.x2 169050jc1 \([1, 1, 0, -242047775, -1901653594875]\) \(-17410957409801706289/7266093465600000\) \(-654493482446630400000000000\) \([]\) \(74027520\) \(3.8535\) \(\Gamma_0(N)\)-optimal
169050.x1 169050jc2 \([1, 1, 0, -21258343775, -1193013861586875]\) \(-11795263402880796810182449/404296875000000\) \(-36417047332763671875000000\) \([]\) \(222082560\) \(4.4028\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 169050.2.a.jc

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