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Properties

Label 8450.x
Number of curves $2$
Conductor $8450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 8450.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8450.x1 8450r2 \([1, 1, 1, -1914858, -1020687049]\) \(-6434774386429585/140608\) \(-16967198996800\) \([]\) \(181440\) \(2.0649\)  
8450.x2 8450r1 \([1, 1, 1, -22058, -1603529]\) \(-9836106385/3407872\) \(-411228681011200\) \([]\) \(60480\) \(1.5156\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8450.x have rank \(0\).

Complex multiplication

The elliptic curves in class 8450.x do not have complex multiplication.

Modular form 8450.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + 5 q^{7} + q^{8} + q^{9} + 3 q^{11} + 2 q^{12} + 5 q^{14} + q^{16} - 3 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.