Properties

Label 40656ba
Number of curves $4$
Conductor $40656$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40656ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40656.di3 40656ba1 \([0, 1, 0, -71023652, -230407834692]\) \(87364831012240243408/1760913\) \(798608587569408\) \([2]\) \(2764800\) \(2.8429\) \(\Gamma_0(N)\)-optimal
40656.di2 40656ba2 \([0, 1, 0, -71026072, -230391350620]\) \(21843440425782779332/3100814593569\) \(5625120975050435798016\) \([2, 2]\) \(5529600\) \(3.1895\)  
40656.di4 40656ba3 \([0, 1, 0, -64622752, -273613760620]\) \(-8226100326647904626/4152140742401883\) \(-15064618200576455166695424\) \([2]\) \(11059200\) \(3.5361\)  
40656.di1 40656ba4 \([0, 1, 0, -77468112, -186113921292]\) \(14171198121996897746/4077720290568771\) \(14794609122673259564095488\) \([4]\) \(11059200\) \(3.5361\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40656ba have rank \(0\).

Complex multiplication

The elliptic curves in class 40656ba do not have complex multiplication.

Modular form 40656.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2q^{5} + q^{7} + q^{9} + 6q^{13} + 2q^{15} + 2q^{17} - 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.