Properties

Label 54978.bj
Number of curves $2$
Conductor $54978$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54978.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54978.bj1 54978bl2 [1, 1, 1, -8919, -327909] [2] 69120  
54978.bj2 54978bl1 [1, 1, 1, -589, -4705] [2] 34560 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54978.bj have rank \(1\).

Complex multiplication

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

Modular form 54978.2.a.bj

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

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.