Properties

Label 5054.b
Number of curves $2$
Conductor $5054$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5054.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5054.b1 5054b2 \([1, -1, 1, -27347262, -55124114227]\) \(-133179212896925841/240518168576\) \(-4084855478516361199616\) \([]\) \(335160\) \(3.0389\)  
5054.b2 5054b1 \([1, -1, 1, 20148, 32163887]\) \(53261199/26353376\) \(-447574222639176416\) \([]\) \(47880\) \(2.0660\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5054.b have rank \(1\).

Complex multiplication

The elliptic curves in class 5054.b do not have complex multiplication.

Modular form 5054.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} - 3 q^{9} + q^{10} - 2 q^{11} - 5 q^{13} + q^{14} + q^{16} - 3 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.