Properties

Label 161700.el
Number of curves 2
Conductor 161700
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("161700.el1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 161700.el

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
161700.el1 161700bc2 [0, 1, 0, -15108, 334788] [2] 552960  
161700.el2 161700bc1 [0, 1, 0, 3267, 40788] [2] 276480 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 161700.el have rank \(1\).

Modular form 161700.2.a.el

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

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 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.