Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54150.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.v1 54150q2 \([1, 0, 1, -91151, -10599802]\) \(781484460931/900\) \(96454687500\) \([2]\) \(184320\) \(1.3917\)  
54150.v2 54150q1 \([1, 0, 1, -5651, -168802]\) \(-186169411/6480\) \(-694473750000\) \([2]\) \(92160\) \(1.0451\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 54150.v do not have complex multiplication.

Modular form 54150.2.a.v

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