Properties

Label 53361.q
Number of curves 6
Conductor 53361
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("53361.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53361.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53361.q1 53361bp6 [1, -1, 1, -241139471, 1441346935592] [2] 7372800  
53361.q2 53361bp4 [1, -1, 1, -15155636, 22258845326] [2, 2] 3686400  
53361.q3 53361bp2 [1, -1, 1, -2082191, -645830314] [2, 2] 1843200  
53361.q4 53361bp1 [1, -1, 1, -1815386, -940703200] [2] 921600 \(\Gamma_0(N)\)-optimal
53361.q5 53361bp5 [1, -1, 1, 1653079, 68913114680] [2] 7372800  
53361.q6 53361bp3 [1, -1, 1, 6722374, -4681842910] [2] 3686400  

Rank

sage: E.rank()
 

The elliptic curves in class 53361.q have rank \(0\).

Modular form 53361.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} - 2q^{5} + 3q^{8} + 2q^{10} + 6q^{13} - q^{16} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.