Properties

Label 271040.bk
Number of curves 4
Conductor 271040
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("271040.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 271040.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
271040.bk1 271040bk4 [0, 1, 0, -202242465, -1075721672225] [2] 79626240  
271040.bk2 271040bk2 [0, 1, 0, -27692705, 55583892703] [2] 26542080  
271040.bk3 271040bk1 [0, 1, 0, -433825, 2140132575] [2] 13271040 \(\Gamma_0(N)\)-optimal
271040.bk4 271040bk3 [0, 1, 0, 3902815, -57652592417] [2] 39813120  

Rank

sage: E.rank()
 

The elliptic curves in class 271040.bk have rank \(1\).

Modular form 271040.2.a.bk

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} + q^{7} + q^{9} - 4q^{13} - 2q^{15} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.