Properties

Label 35739n
Number of curves 2
Conductor 35739
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35739.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35739n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.k2 35739n1 [0, 0, 1, -1180470, -532184666] [] 518400 \(\Gamma_0(N)\)-optimal
35739.k1 35739n2 [0, 0, 1, -97675770, -371559508025] [] 1555200  

Rank

sage: E.rank()
 

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

Modular form 35739.2.a.k

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

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.