Properties

Label 53361.bz
Number of curves $2$
Conductor $53361$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 53361.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53361.bz1 53361bt2 \([0, 0, 1, -993531, 381477577]\) \(-1713910976512/1594323\) \(-100891837250259363\) \([]\) \(873600\) \(2.1856\)  
53361.bz2 53361bt1 \([0, 0, 1, -2541, -53573]\) \(-28672/3\) \(-189845791443\) \([]\) \(67200\) \(0.90317\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 53361.2.a.bz

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{10} + q^{13} - 4 q^{16} + q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.