Properties

Label 588.c
Number of curves $4$
Conductor $588$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("588.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 588.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
588.c1 588b4 [0, -1, 0, -89588, 10350936] [2] 1728  
588.c2 588b3 [0, -1, 0, -5553, 165894] [2] 864  
588.c3 588b2 [0, -1, 0, -1388, 6840] [2] 576  
588.c4 588b1 [0, -1, 0, 327, 666] [2] 288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 588.c have rank \(1\).

Modular form 588.2.a.c

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.