Properties

Label 35574by
Number of curves 4
Conductor 35574
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35574.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35574by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35574.bu3 35574by1 [1, 1, 1, -32733, 2136399] [2] 172800 \(\Gamma_0(N)\)-optimal
35574.bu4 35574by2 [1, 1, 1, 26557, 9085187] [2] 345600  
35574.bu1 35574by3 [1, 1, 1, -477408, -126677055] [2] 518400  
35574.bu2 35574by4 [1, 1, 1, -240248, -252276991] [2] 1036800  

Rank

sage: E.rank()
 

The elliptic curves in class 35574by have rank \(0\).

Modular form 35574.2.a.bu

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - q^{12} - 4q^{13} + q^{16} - 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.