Properties

Label 224400fd
Number of curves 6
Conductor 224400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("224400.co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 224400fd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.co4 224400fd1 [0, -1, 0, -2924008, -1923513488] [2] 3538944 \(\Gamma_0(N)\)-optimal
224400.co3 224400fd2 [0, -1, 0, -2956008, -1879225488] [2, 2] 7077888  
224400.co2 224400fd3 [0, -1, 0, -7956008, 6160774512] [2, 2] 14155776  
224400.co5 224400fd4 [0, -1, 0, 1531992, -7085305488] [2] 14155776  
224400.co1 224400fd5 [0, -1, 0, -116856008, 486191974512] [2] 28311552  
224400.co6 224400fd6 [0, -1, 0, 20943992, 40609574512] [2] 28311552  

Rank

sage: E.rank()
 

The elliptic curves in class 224400fd have rank \(1\).

Modular form 224400.2.a.co

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.