Properties

Label 1584q
Number of curves 4
Conductor 1584
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1584.o1")
sage: E.isogeny_class()

Elliptic curves in class 1584q

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1584.o3 1584q1 [0, 0, 0, -939, -10982] 2 768 \(\Gamma_0(N)\)-optimal
1584.o2 1584q2 [0, 0, 0, -1659, 8170] 4 1536  
1584.o1 1584q3 [0, 0, 0, -21099, 1178458] 4 3072  
1584.o4 1584q4 [0, 0, 0, 6261, 63610] 2 3072  

Rank

sage: E.rank()

The elliptic curves in class 1584q have rank \(0\).

Modular form 1584.2.a.o

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.