Properties

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

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Show commands: SageMath
E = EllipticCurve("ej1")
 
E.isogeny_class()
 

Elliptic curves in class 161700.ej

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.ej1 161700bb2 \([0, 1, 0, -23508, 527988]\) \(1047213232/515625\) \(707437500000000\) \([2]\) \(552960\) \(1.5426\)  
161700.ej2 161700bb1 \([0, 1, 0, 5367, 65988]\) \(199344128/136125\) \(-11672718750000\) \([2]\) \(276480\) \(1.1960\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 161700.ej do not have complex multiplication.

Modular form 161700.2.a.ej

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