Properties

Label 54080bp
Number of curves $2$
Conductor $54080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 54080bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54080.s1 54080bp1 \([0, 1, 0, -13745, -615185]\) \(3631696/65\) \(5140358512640\) \([2]\) \(86016\) \(1.2347\) \(\Gamma_0(N)\)-optimal
54080.s2 54080bp2 \([0, 1, 0, -225, -1758977]\) \(-4/4225\) \(-1336493213286400\) \([2]\) \(172032\) \(1.5813\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54080bp have rank \(0\).

Complex multiplication

The elliptic curves in class 54080bp do not have complex multiplication.

Modular form 54080.2.a.bp

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} + q^{9} + 2 q^{11} - 2 q^{15} + 2 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.