Properties

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

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 161700.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.bh1 161700ej2 \([0, -1, 0, -2229908, -1233767688]\) \(2605772594896/108945375\) \(51269257693500000000\) \([2]\) \(3981312\) \(2.5468\)  
161700.bh2 161700ej1 \([0, -1, 0, 66967, -71548938]\) \(1129201664/75796875\) \(-2229356636718750000\) \([2]\) \(1990656\) \(2.2003\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 161700.2.a.bh

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