Properties

Label 35a
Number of curves 3
Conductor 35
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("35.a1")
sage: E.isogeny_class()

Elliptic curves in class 35a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
35.a3 35a1 [0, 1, 1, 9, 1] 3 2 \(\Gamma_0(N)\)-optimal
35.a1 35a2 [0, 1, 1, -131, -650] 1 6  
35.a2 35a3 [0, 1, 1, -1, 0] 3 6  

Rank

sage: E.rank()

The elliptic curves in class 35a have rank \(0\).

Modular form 35.2.a.a

sage: E.q_eigenform(10)
\( q + q^{3} - 2q^{4} - q^{5} + q^{7} - 2q^{9} - 3q^{11} - 2q^{12} + 5q^{13} - q^{15} + 4q^{16} + 3q^{17} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.