Properties

Label 48.a
Number of curves 6
Conductor \(48\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("48.a1")
sage: E.isogeny_class()

Elliptic curves in class 48.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
48.a1 48a5 [0, 1, 0, -384, 2772] 4 8  
48.a2 48a2 [0, 1, 0, -64, -220] 2 4  
48.a3 48a3 [0, 1, 0, -24, 36] 8 4  
48.a4 48a1 [0, 1, 0, -4, -4] 4 2 \(\Gamma_0(N)\)-optimal
48.a5 48a4 [0, 1, 0, 1, 0] 2 4  
48.a6 48a6 [0, 1, 0, 16, 180] 8 8  

Rank

sage: E.rank()

The elliptic curves in class 48.a have rank \(0\).

Modular form 48.2.1.a

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

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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