Properties

Label 224400hy
Number of curves 2
Conductor 224400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("224400.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 224400hy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.bd2 224400hy1 [0, -1, 0, -5339408, 4693671312] [2] 9289728 \(\Gamma_0(N)\)-optimal
224400.bd1 224400hy2 [0, -1, 0, -10252408, -5289544688] [2] 18579456  

Rank

sage: E.rank()
 

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

Modular form 224400.2.a.bd

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

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.