Properties

Label 30.a
Number of curves 8
Conductor \(30\)
CM False
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("30.a1")
sage: E.isogeny_class()

Elliptic curves in class 30.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
30.a1 30a7 [1, 0, 1, -5334, -150368] 2 24  
30.a2 30a8 [1, 0, 1, -454, -544] 2 24  
30.a3 30a6 [1, 0, 1, -334, -2368] 4 12  
30.a4 30a5 [1, 0, 1, -289, 1862] 6 8  
30.a5 30a4 [1, 0, 1, -69, -194] 6 8  
30.a6 30a2 [1, 0, 1, -19, 26] 12 4  
30.a7 30a3 [1, 0, 1, -14, -64] 2 6  
30.a8 30a1 [1, 0, 1, 1, 2] 6 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 30.a have rank \(0\).

Modular form 30.2.1.a

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

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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