Properties

Label 162450ey
Number of curves $2$
Conductor $162450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ey1")
 
E.isogeny_class()
 

Elliptic curves in class 162450ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162450.bs2 162450ey1 \([1, -1, 0, 729333, -165843259]\) \(2161700757/1848320\) \(-36684496168560000000\) \([2]\) \(5529600\) \(2.4417\) \(\Gamma_0(N)\)-optimal
162450.bs1 162450ey2 \([1, -1, 0, -3602667, -1461111259]\) \(260549802603/104256800\) \(2069234862007837500000\) \([2]\) \(11059200\) \(2.7882\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162450ey have rank \(0\).

Complex multiplication

The elliptic curves in class 162450ey do not have complex multiplication.

Modular form 162450.2.a.ey

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