Properties

Label 131648.bt
Number of curves $4$
Conductor $131648$
CM no
Rank $0$
Graph

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

Elliptic curves in class 131648.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
131648.bt1 131648ch3 \([0, 0, 0, -702284, 226525552]\) \(82483294977/17\) \(7894869475328\) \([2]\) \(737280\) \(1.8620\)  
131648.bt2 131648ch2 \([0, 0, 0, -44044, 3513840]\) \(20346417/289\) \(134212781080576\) \([2, 2]\) \(368640\) \(1.5155\)  
131648.bt3 131648ch1 \([0, 0, 0, -5324, -63888]\) \(35937/17\) \(7894869475328\) \([2]\) \(184320\) \(1.1689\) \(\Gamma_0(N)\)-optimal
131648.bt4 131648ch4 \([0, 0, 0, -5324, 9476720]\) \(-35937/83521\) \(-38787493732286464\) \([2]\) \(737280\) \(1.8620\)  

Rank

sage: E.rank()
 

The elliptic curves in class 131648.bt have rank \(0\).

Complex multiplication

The elliptic curves in class 131648.bt do not have complex multiplication.

Modular form 131648.2.a.bt

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - 4 q^{7} - 3 q^{9} - 2 q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) 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.