Properties

Label 161700bi
Number of curves $4$
Conductor $161700$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 161700bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.et4 161700bi1 \([0, 1, 0, 267867, 196153488]\) \(72268906496/606436875\) \(-17836672976718750000\) \([2]\) \(2488320\) \(2.3753\) \(\Gamma_0(N)\)-optimal
161700.et3 161700bi2 \([0, 1, 0, -3866508, 2693315988]\) \(13584145739344/1195803675\) \(562740426240300000000\) \([2]\) \(4976640\) \(2.7219\)  
161700.et2 161700bi3 \([0, 1, 0, -19136133, 32239433988]\) \(-26348629355659264/24169921875\) \(-710891784667968750000\) \([2]\) \(7464960\) \(2.9247\)  
161700.et1 161700bi4 \([0, 1, 0, -306245508, 2062676933988]\) \(6749703004355978704/5671875\) \(2669161687500000000\) \([2]\) \(14929920\) \(3.2712\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 161700.2.a.bi

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.