Properties

Label 103488.bl
Number of curves 6
Conductor 103488
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("103488.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 103488.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
103488.bl1 103488cb6 [0, -1, 0, -14171649, 20538957825] [2] 3932160  
103488.bl2 103488cb4 [0, -1, 0, -890689, 317368129] [2, 2] 1966080  
103488.bl3 103488cb2 [0, -1, 0, -122369, -9167871] [2, 2] 983040  
103488.bl4 103488cb1 [0, -1, 0, -106689, -13373247] [2] 491520 \(\Gamma_0(N)\)-optimal
103488.bl5 103488cb5 [0, -1, 0, 97151, 981789313] [2] 3932160  
103488.bl6 103488cb3 [0, -1, 0, 395071, -66810687] [2] 1966080  

Rank

sage: E.rank()
 

The elliptic curves in class 103488.bl have rank \(1\).

Modular form 103488.2.a.bl

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{5} + q^{9} + q^{11} + 6q^{13} + 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.