Properties

Label 35739h
Number of curves 2
Conductor 35739
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35739.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35739h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.r1 35739h1 [1, -1, 0, -1122, -12817] [2] 25920 \(\Gamma_0(N)\)-optimal
35739.r2 35739h2 [1, -1, 0, 1443, -64630] [2] 51840  

Rank

sage: E.rank()
 

The elliptic curves in class 35739h have rank \(0\).

Modular form 35739.2.a.r

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 4q^{7} - 3q^{8} + q^{11} + 4q^{13} - 4q^{14} - q^{16} + 4q^{17} + O(q^{20}) \)

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 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.