Properties

Label 55440.eh
Number of curves 4
Conductor 55440
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55440.eh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55440.eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55440.eh1 55440en4 [0, 0, 0, -4750707, 3985475506] [2] 1179648  
55440.eh2 55440en2 [0, 0, 0, -305427, 58515154] [2, 2] 589824  
55440.eh3 55440en1 [0, 0, 0, -72147, -6476654] [2] 294912 \(\Gamma_0(N)\)-optimal
55440.eh4 55440en3 [0, 0, 0, 407373, 291030514] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 55440.eh have rank \(1\).

Modular form 55440.2.a.eh

sage: E.q_eigenform(10)
 
\( q + q^{5} + q^{7} - q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.