Properties

Label 267696bj
Number of curves $6$
Conductor $267696$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("267696.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 267696bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
267696.bj5 267696bj1 [0, 0, 0, -584571, 246771434] [2] 5505024 \(\Gamma_0(N)\)-optimal
267696.bj4 267696bj2 [0, 0, 0, -10440651, 12982798010] [2, 2] 11010048  
267696.bj1 267696bj3 [0, 0, 0, -167042811, 830978520554] [2] 22020096  
267696.bj3 267696bj4 [0, 0, 0, -11535771, 10092776330] [2, 2] 22020096  
267696.bj6 267696bj5 [0, 0, 0, 32634069, 68776825754] [2] 44040192  
267696.bj2 267696bj6 [0, 0, 0, -73227531, -233552660614] [2] 44040192  

Rank

sage: E.rank()
 

The elliptic curves in class 267696bj have rank \(0\).

Modular form 267696.2.a.bj

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + q^{11} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.