Properties

Label 284592.ka
Number of curves 4
Conductor 284592
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("284592.ka1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 284592.ka

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
284592.ka1 284592ka4 [0, 1, 0, -4175992, -3286028572] [2] 6635520  
284592.ka2 284592ka3 [0, 1, 0, -618592, 115415012] [2] 6635520  
284592.ka3 284592ka2 [0, 1, 0, -262852, -50644420] [2, 2] 3317760  
284592.ka4 284592ka1 [0, 1, 0, 3953, -2619520] [2] 1658880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 284592.ka have rank \(0\).

Modular form 284592.2.a.ka

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + q^{9} + 6q^{13} + 2q^{15} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.