Properties

Label 33.a
Number of curves 4
Conductor \(33\)
CM False
Rank \(0\)
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("33.a1")
sage: E.isogeny_class()

Elliptic curves in class 33.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
33.a1 33a3 [1, 1, 0, -146, 621] 4 6  
33.a2 33a1 [1, 1, 0, -11, 0] 4 3 \(\Gamma_0(N)\)-optimal
33.a3 33a2 [1, 1, 0, -6, -9] 2 6  
33.a4 33a4 [1, 1, 0, 44, 55] 2 6  

Rank

sage: E.rank()

The elliptic curves in class 33.a have rank \(0\).

Modular form 33.2.1.a

sage: E.q_eigenform(10)
\( q + q^{2} - q^{3} - q^{4} - 2q^{5} - q^{6} + 4q^{7} - 3q^{8} + q^{9} + O(q^{10}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

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

Isogeny graph

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