Properties

Label 103488de
Number of curves 2
Conductor 103488
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("103488.ht1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 103488de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
103488.ht2 103488de1 [0, 1, 0, 523, 2715] [2] 69120 \(\Gamma_0(N)\)-optimal
103488.ht1 103488de2 [0, 1, 0, -2417, 20943] [2] 138240  

Rank

sage: E.rank()
 

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

Modular form 103488.2.a.ht

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.