Properties

Label 134640cd
Number of curves 6
Conductor 134640
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("134640.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 134640cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
134640.be4 134640cd1 [0, 0, 0, -1052643, 415689442] [2] 1179648 \(\Gamma_0(N)\)-optimal
134640.be3 134640cd2 [0, 0, 0, -1064163, 406125538] [2, 2] 2359296  
134640.be5 134640cd3 [0, 0, 0, 551517, 1530315682] [2] 4718592  
134640.be2 134640cd4 [0, 0, 0, -2864163, -1330154462] [2, 2] 4718592  
134640.be6 134640cd5 [0, 0, 0, 7539837, -8773176062] [2] 9437184  
134640.be1 134640cd6 [0, 0, 0, -42068163, -105009052862] [2] 9437184  

Rank

sage: E.rank()
 

The elliptic curves in class 134640cd have rank \(1\).

Modular form 134640.2.a.be

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{11} + 6q^{13} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.