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Properties

Label 54978.bs
Number of curves $2$
Conductor $54978$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 54978.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54978.bs1 54978bo1 \([1, 1, 1, -44297, -3578569]\) \(81706955619457/744505344\) \(87590309216256\) \([2]\) \(322560\) \(1.4975\) \(\Gamma_0(N)\)-optimal
54978.bs2 54978bo2 \([1, 1, 1, -12937, -8508361]\) \(-2035346265217/264305213568\) \(-31095244071061632\) \([2]\) \(645120\) \(1.8441\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54978.bs have rank \(0\).

Complex multiplication

The elliptic curves in class 54978.bs do not have complex multiplication.

Modular form 54978.2.a.bs

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} + q^{8} + q^{9} + 2 q^{10} - q^{11} - q^{12} + 4 q^{13} - 2 q^{15} + q^{16} + q^{17} + q^{18} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.