Properties

Label 504.c
Number of curves $4$
Conductor $504$
CM no
Rank $0$
Graph

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

Elliptic curves in class 504.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
504.c1 504c3 [0, 0, 0, -2691, -53730] [2] 256  
504.c2 504c4 [0, 0, 0, -531, 3726] [2] 256  
504.c3 504c2 [0, 0, 0, -171, -810] [2, 2] 128  
504.c4 504c1 [0, 0, 0, 9, -54] [2] 64 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 504.c have rank \(0\).

Complex multiplication

The elliptic curves in class 504.c do not have complex multiplication.

Modular form 504.2.a.c

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

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.