Properties

Label 53361bm
Number of curves $2$
Conductor $53361$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53361bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53361.r2 53361bm1 [1, -1, 1, -1112, -55492] [] 51840 \(\Gamma_0(N)\)-optimal
53361.r1 53361bm2 [1, -1, 1, -1601942, 780829382] [] 570240  

Rank

sage: E.rank()
 

The elliptic curves in class 53361bm have rank \(2\).

Complex multiplication

The elliptic curves in class 53361bm do not have complex multiplication.

Modular form 53361.2.a.bm

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

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.