Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("103488.ih1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 103488.ih

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
103488.ih1 103488in4 [0, 1, 0, -92577, 10809567] [2] 393216  
103488.ih2 103488in2 [0, 1, 0, -6337, 133055] [2, 2] 196608  
103488.ih3 103488in1 [0, 1, 0, -2417, -44913] [2] 98304 \(\Gamma_0(N)\)-optimal
103488.ih4 103488in3 [0, 1, 0, 17183, 909215] [2] 393216  

Rank

sage: E.rank()
 

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

Modular form 103488.2.a.ih

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.