Properties

Label 119952.bt
Number of curves $4$
Conductor $119952$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bt1 119952gp4 \([0, 0, 0, -35837571, -82576372606]\) \(14489843500598257/6246072\) \(2194232798931812352\) \([2]\) \(7077888\) \(2.8620\)  
119952.bt2 119952gp3 \([0, 0, 0, -4791171, 2133673346]\) \(34623662831857/14438442312\) \(5072196363806768136192\) \([2]\) \(7077888\) \(2.8620\)  
119952.bt3 119952gp2 \([0, 0, 0, -2251011, -1276745470]\) \(3590714269297/73410624\) \(25789007710902288384\) \([2, 2]\) \(3538944\) \(2.5154\)  
119952.bt4 119952gp1 \([0, 0, 0, 6909, -59726590]\) \(103823/4386816\) \(-1541079825861574656\) \([2]\) \(1769472\) \(2.1688\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 119952.bt have rank \(1\).

Complex multiplication

The elliptic curves in class 119952.bt do not have complex multiplication.

Modular form 119952.2.a.bt

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.