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Properties

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

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 53361.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53361.bu1 53361bh2 \([1, -1, 0, -134514, 74263041]\) \(-121\) \(-2224552296757742721\) \([]\) \(570240\) \(2.2032\)  
53361.bu2 53361bh1 \([1, -1, 0, -13239, -583038]\) \(-24729001\) \(-10377700641\) \([]\) \(51840\) \(1.0043\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 53361.2.a.bu

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.