Properties

Label 87360.bl
Number of curves 8
Conductor 87360
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("87360.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87360.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
87360.bl1 87360m8 [0, -1, 0, -2572189121, -50210557479999] [2] 21233664  
87360.bl2 87360m6 [0, -1, 0, -160761921, -784498732479] [2, 2] 10616832  
87360.bl3 87360m7 [0, -1, 0, -158786241, -804722188095] [2] 21233664  
87360.bl4 87360m5 [0, -1, 0, -31769921, -68800473279] [2] 7077888  
87360.bl5 87360m3 [0, -1, 0, -10171201, -11938220735] [2] 5308416  
87360.bl6 87360m2 [0, -1, 0, -2649921, -292761279] [2, 2] 3538944  
87360.bl7 87360m1 [0, -1, 0, -1646401, 809304385] [2] 1769472 \(\Gamma_0(N)\)-optimal
87360.bl8 87360m4 [0, -1, 0, 10413759, -2333308095] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 87360.bl have rank \(0\).

Modular form 87360.2.a.bl

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{7} + q^{9} - q^{13} + q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.