Properties

Label 283920.bl
Number of curves 8
Conductor 283920
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("283920.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 283920.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.bl1 283920bl7 [0, -1, 0, -949732736, 11265810186240] [2] 63700992  
283920.bl2 283920bl6 [0, -1, 0, -59359616, 176034902016] [2, 2] 31850496  
283920.bl3 283920bl8 [0, -1, 0, -55033216, 202778976256] [2] 63700992  
283920.bl4 283920bl4 [0, -1, 0, -11782736, 15297666240] [2] 21233664  
283920.bl5 283920bl3 [0, -1, 0, -3981696, 2325442560] [2] 15925248  
283920.bl6 283920bl2 [0, -1, 0, -1561616, -393797184] [2, 2] 10616832  
283920.bl7 283920bl1 [0, -1, 0, -1345296, -599906880] [2] 5308416 \(\Gamma_0(N)\)-optimal
283920.bl8 283920bl5 [0, -1, 0, 5198384, -2897701184] [2] 21233664  

Rank

sage: E.rank()
 

The elliptic curves in class 283920.bl have rank \(1\).

Modular form 283920.2.a.bl

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{7} + q^{9} + q^{15} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.