Properties

Label 333795k
Number of curves $6$
Conductor $333795$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 333795k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
333795.k6 333795k1 [1, 1, 1, 10109, -113637976] [2] 4915200 \(\Gamma_0(N)\)-optimal
333795.k5 333795k2 [1, 1, 1, -3459336, -2434002792] [2, 2] 9830400  
333795.k4 333795k3 [1, 1, 1, -7353611, 4044513098] [2] 19660800  
333795.k2 333795k4 [1, 1, 1, -55076181, -157346478006] [2, 2] 19660800  
333795.k3 333795k5 [1, 1, 1, -54803076, -158983797102] [2] 39321600  
333795.k1 333795k6 [1, 1, 1, -881218806, -10069075235706] [2] 39321600  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 333795.2.a.k

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.