Properties

Label 13552c
Number of curves $4$
Conductor $13552$
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 13552c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13552.p4 13552c1 [0, 0, 0, 121, 2662] [2] 5120 \(\Gamma_0(N)\)-optimal
13552.p3 13552c2 [0, 0, 0, -2299, 39930] [2, 2] 10240  
13552.p2 13552c3 [0, 0, 0, -7139, -183678] [2] 20480  
13552.p1 13552c4 [0, 0, 0, -36179, 2648690] [2] 20480  

Rank

sage: E.rank()
 

The elliptic curves in class 13552c have rank \(0\).

Complex multiplication

The elliptic curves in class 13552c do not have complex multiplication.

Modular form 13552.2.a.c

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

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 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.