Properties

Label 101640.bx
Number of curves $4$
Conductor $101640$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 101640.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101640.bx1 101640cm4 \([0, 1, 0, -597296, 177476880]\) \(12990838708516/144375\) \(261907578240000\) \([2]\) \(737280\) \(1.9200\)  
101640.bx2 101640cm2 \([0, 1, 0, -38276, 2615424]\) \(13674725584/1334025\) \(605006505734400\) \([2, 2]\) \(368640\) \(1.5735\)  
101640.bx3 101640cm1 \([0, 1, 0, -8631, -266070]\) \(2508888064/396165\) \(11229287417040\) \([2]\) \(184320\) \(1.2269\) \(\Gamma_0(N)\)-optimal
101640.bx4 101640cm3 \([0, 1, 0, 46424, 12643904]\) \(6099383804/41507235\) \(-75297381113687040\) \([2]\) \(737280\) \(1.9200\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101640.bx have rank \(1\).

Complex multiplication

The elliptic curves in class 101640.bx do not have complex multiplication.

Modular form 101640.2.a.bx

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} - 2 q^{13} - q^{15} - 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.