Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("35739.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35739j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.g2 35739j1 [1, -1, 1, -5483, -27566] [2] 78624 \(\Gamma_0(N)\)-optimal
35739.g1 35739j2 [1, -1, 1, -54218, 4845934] [2] 157248  

Rank

sage: E.rank()
 

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

Modular form 35739.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} + 4q^{5} - 2q^{7} + 3q^{8} - 4q^{10} + q^{11} + 2q^{13} + 2q^{14} - q^{16} - 2q^{17} + O(q^{20}) \)

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 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.