Properties

Label 103488ff
Number of curves 4
Conductor 103488
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("103488.ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 103488ff

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
103488.ca3 103488ff1 [0, -1, 0, -17313, 832833] [2] 276480 \(\Gamma_0(N)\)-optimal
103488.ca4 103488ff2 [0, -1, 0, 14047, 3485889] [2] 552960  
103488.ca1 103488ff3 [0, -1, 0, -252513, -48568575] [2] 829440  
103488.ca2 103488ff4 [0, -1, 0, -127073, -96963327] [2] 1658880  

Rank

sage: E.rank()
 

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

Modular form 103488.2.a.ca

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.