Properties

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

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 161700.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.bg1 161700ei2 \([0, -1, 0, -120808887908, 16122197816028312]\) \(414354576760345737269208016/1182266314178222109375\) \(556369798387014611783437500000000\) \([2]\) \(1006387200\) \(5.1547\)  
161700.bg2 161700ei1 \([0, -1, 0, -4529591033, 455423030872062]\) \(-349439858058052607328256/2844147488104248046875\) \(-83652776956994169616699218750000\) \([2]\) \(503193600\) \(4.8081\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 161700.2.a.bg

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