Properties

Label 163254.bs
Number of curves $4$
Conductor $163254$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 163254.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163254.bs1 163254ck4 \([1, 0, 1, -30225485, -63962454814]\) \(632678989847546725777/80515134\) \(388631173427406\) \([2]\) \(8847360\) \(2.6595\)  
163254.bs2 163254ck3 \([1, 0, 1, -2161345, -692760742]\) \(231331938231569617/90942310746882\) \(438961163993846759538\) \([2]\) \(8847360\) \(2.6595\)  
163254.bs3 163254ck2 \([1, 0, 1, -1889255, -999351754]\) \(154502321244119857/55101928644\) \(265966485096216996\) \([2, 2]\) \(4423680\) \(2.3129\)  
163254.bs4 163254ck1 \([1, 0, 1, -101235, -20232002]\) \(-23771111713777/22848457968\) \(-110285142556064112\) \([2]\) \(2211840\) \(1.9663\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 163254.bs have rank \(0\).

Complex multiplication

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

Modular form 163254.2.a.bs

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - 2 q^{10} - 4 q^{11} + q^{12} - q^{14} + 2 q^{15} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.