Properties

Label 35739.a
Number of curves 3
Conductor 35739
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35739.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35739.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.a1 35739r3 [0, 0, 1, -25408263, -49295874780] [] 1080000  
35739.a2 35739r2 [0, 0, 1, -33573, -4288590] [] 216000  
35739.a3 35739r1 [0, 0, 1, -1083, 32580] [] 43200 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35739.a have rank \(1\).

Modular form 35739.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{2} + 2q^{4} - q^{5} - 2q^{7} + 2q^{10} - q^{11} - 4q^{13} + 4q^{14} - 4q^{16} + 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.