Properties

Label 34.a
Number of curves 4
Conductor \(34\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("34.a1")
sage: E.isogeny_class()

Elliptic curves in class 34.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
34.a1 34a4 [1, 0, 0, -113, -329] 2 12  
34.a2 34a3 [1, 0, 0, -103, -411] 2 6  
34.a3 34a2 [1, 0, 0, -43, 105] 6 4  
34.a4 34a1 [1, 0, 0, -3, 1] 6 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 34.a have rank \(0\).

Modular form 34.2.1.a

sage: E.q_eigenform(10)
\( q + q^{2} - 2q^{3} + q^{4} - 2q^{6} - 4q^{7} + q^{8} + q^{9} + 6q^{11} - 2q^{12} + 2q^{13} - 4q^{14} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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