Properties

Label 54150t
Number of curves $2$
Conductor $54150$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54150.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54150t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54150.bk2 54150t1 [1, 0, 1, -21330776, 1919420198] [2] 14008320 \(\Gamma_0(N)\)-optimal
54150.bk1 54150t2 [1, 0, 1, -240818776, 1434737084198] [2] 28016640  

Rank

sage: E.rank()
 

The elliptic curves in class 54150t have rank \(0\).

Modular form 54150.2.a.bk

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} + 4q^{7} - q^{8} + q^{9} + 6q^{11} + q^{12} - 4q^{13} - 4q^{14} + q^{16} - 6q^{17} - q^{18} + O(q^{20}) \)

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 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.