Properties

Label 224400ek
Number of curves 2
Conductor 224400
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("224400.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 224400ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.p2 224400ek1 [0, -1, 0, 16367, 1432012] [2] 1013760 \(\Gamma_0(N)\)-optimal
224400.p1 224400ek2 [0, -1, 0, -135508, 16012012] [2] 2027520  

Rank

sage: E.rank()
 

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

Modular form 224400.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{3} - 4q^{7} + q^{9} + q^{11} + 4q^{13} + q^{17} - 6q^{19} + O(q^{20}) \)

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.