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Properties

Label 163254bu
Number of curves $2$
Conductor $163254$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 163254bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163254.cy2 163254bu1 \([1, 1, 1, 56358, 11924583]\) \(4101378352343/15049939968\) \(-72643185687002112\) \([2]\) \(2073600\) \(1.9182\) \(\Gamma_0(N)\)-optimal
163254.cy1 163254bu2 \([1, 1, 1, -565562, 142776551]\) \(4144806984356137/568114785504\) \(2742181559703776736\) \([2]\) \(4147200\) \(2.2648\)  

Rank

sage: E.rank()
 

The elliptic curves in class 163254bu have rank \(1\).

Complex multiplication

The elliptic curves in class 163254bu do not have complex multiplication.

Modular form 163254.2.a.bu

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + 2 q^{10} - q^{12} + q^{14} - 2 q^{15} + q^{16} + q^{18} - 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.