Properties

Label 13552.p
Number of curves $4$
Conductor $13552$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13552.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13552.p1 13552c4 \([0, 0, 0, -36179, 2648690]\) \(1443468546/7\) \(25397098496\) \([2]\) \(20480\) \(1.1969\)  
13552.p2 13552c3 \([0, 0, 0, -7139, -183678]\) \(11090466/2401\) \(8711204784128\) \([2]\) \(20480\) \(1.1969\)  
13552.p3 13552c2 \([0, 0, 0, -2299, 39930]\) \(740772/49\) \(88889844736\) \([2, 2]\) \(10240\) \(0.85034\)  
13552.p4 13552c1 \([0, 0, 0, 121, 2662]\) \(432/7\) \(-3174637312\) \([2]\) \(5120\) \(0.50377\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13552.2.a.p

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

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.