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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 333795j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333795.j1 333795j1 \([1, 1, 1, -282023546, 1822837858718]\) \(102774717221250741791041/35873574515625\) \(865900880147540015625\) \([2]\) \(52531200\) \(3.3728\) \(\Gamma_0(N)\)-optimal
333795.j2 333795j2 \([1, 1, 1, -280759171, 1839993404468]\) \(-101398618530122836361041/1920990187890340875\) \(-46368033208526067303832875\) \([2]\) \(105062400\) \(3.7194\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 333795.2.a.j

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