Properties

Label 333795.n
Number of curves $2$
Conductor $333795$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 333795.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333795.n1 333795n2 \([1, 1, 1, -99390421, 380275104518]\) \(22100929481998139979094433/71639755865687411325\) \(351966120568122251839725\) \([2]\) \(74280960\) \(3.3840\)  
333795.n2 333795n1 \([1, 1, 1, -3565076, 11040885164]\) \(-1019960453167729894673/10131394987524330135\) \(-49775543573707033953255\) \([2]\) \(37140480\) \(3.0374\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 333795.n have rank \(0\).

Complex multiplication

The elliptic curves in class 333795.n do not have complex multiplication.

Modular form 333795.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{7} + 3 q^{8} + q^{9} + q^{10} - q^{11} + q^{12} + 6 q^{13} - q^{14} + q^{15} - q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.