Properties

Label 56.a
Number of curves 4
Conductor 56
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("56.a1")
sage: E.isogeny_class()

Elliptic curves in class 56.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
56.a1 56a4 [0, 0, 0, -299, 1990] 2 8  
56.a2 56a3 [0, 0, 0, -59, -138] 2 8  
56.a3 56a2 [0, 0, 0, -19, 30] 4 4  
56.a4 56a1 [0, 0, 0, 1, 2] 4 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 56.a have rank \(0\).

Modular form 56.2.a.a

sage: E.q_eigenform(10)
\( q + 2q^{5} - q^{7} - 3q^{9} - 4q^{11} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.