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Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 333795.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333795.p1 333795p2 \([1, 1, 1, -2016070, -1102647418]\) \(7641880721873/17325\) \(2054534960310525\) \([2]\) \(4526080\) \(2.1825\)  
333795.p2 333795p1 \([1, 1, 1, -124565, -17680150]\) \(-1802485313/88935\) \(-10546612796260695\) \([2]\) \(2263040\) \(1.8360\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 333795.2.a.p

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