Properties

Label 138600.bd
Number of curves $4$
Conductor $138600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 138600.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
138600.bd1 138600eo4 \([0, 0, 0, -144052275, 471861256750]\) \(14171198121996897746/4077720290568771\) \(95125058938388289888000000\) \([2]\) \(47185920\) \(3.6912\)  
138600.bd2 138600eo2 \([0, 0, 0, -132073275, 584140423750]\) \(21843440425782779332/3100814593569\) \(36167901419388816000000\) \([2, 2]\) \(23592960\) \(3.3446\)  
138600.bd3 138600eo1 \([0, 0, 0, -132068775, 584182224250]\) \(87364831012240243408/1760913\) \(5134822308000000\) \([2]\) \(11796480\) \(2.9980\) \(\Gamma_0(N)\)-optimal
138600.bd4 138600eo3 \([0, 0, 0, -120166275, 693744358750]\) \(-8226100326647904626/4152140742401883\) \(-96861139238751126624000000\) \([2]\) \(47185920\) \(3.6912\)  

Rank

sage: E.rank()
 

The elliptic curves in class 138600.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 138600.bd do not have complex multiplication.

Modular form 138600.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{7} - q^{11} + 6q^{13} - 2q^{17} - 8q^{19} + O(q^{20})\)  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 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.