Properties

Label 224400hq
Number of curves 4
Conductor 224400
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("224400.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 224400hq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.n3 224400hq1 [0, -1, 0, -715308, -232617888] [2] 1572864 \(\Gamma_0(N)\)-optimal
224400.n2 224400hq2 [0, -1, 0, -715808, -232275888] [2, 2] 3145728  
224400.n1 224400hq3 [0, -1, 0, -1012808, -20811888] [2] 6291456  
224400.n4 224400hq4 [0, -1, 0, -426808, -421859888] [2] 6291456  

Rank

sage: E.rank()
 

The elliptic curves in class 224400hq have rank \(0\).

Modular form 224400.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{3} - 4q^{7} + q^{9} + q^{11} - 2q^{13} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.