Properties

Label 35739.t
Number of curves 4
Conductor 35739
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("35739.t1")
sage: E.isogeny_class()

Elliptic curves in class 35739.t

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
35739.t1 35739q4 [1, -1, 0, -476046, 126416565] 2 345600  
35739.t2 35739q2 [1, -1, 0, -37431, 884952] 4 172800  
35739.t3 35739q1 [1, -1, 0, -21186, -1171665] 2 86400 \(\Gamma_0(N)\)-optimal
35739.t4 35739q3 [1, -1, 0, 141264, 6781887] 2 345600  

Rank

sage: E.rank()

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

Modular form 35739.2.a.t

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.