Properties

Label 184590q
Number of curves 2
Conductor 184590
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("184590.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 184590q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
184590.f2 184590q1 [1, -1, 0, 86295, -63082675] [] 5531904 \(\Gamma_0(N)\)-optimal
184590.f1 184590q2 [1, -1, 0, -49913655, 135823538195] [] 38723328  

Rank

sage: E.rank()
 

The elliptic curves in class 184590q have rank \(0\).

Modular form 184590.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 5q^{11} + 7q^{13} - q^{14} + q^{16} + 3q^{17} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.