Properties

Label 333270bv
Number of curves $6$
Conductor $333270$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("333270.bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 333270bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
333270.bv6 333270bv1 [1, -1, 0, 47511, -5590067] [2] 2883584 \(\Gamma_0(N)\)-optimal
333270.bv5 333270bv2 [1, -1, 0, -333369, -57618275] [2, 2] 5767168  
333270.bv4 333270bv3 [1, -1, 0, -1761669, 851066185] [2] 11534336  
333270.bv2 333270bv4 [1, -1, 0, -4999149, -4300678607] [2, 2] 11534336  
333270.bv3 333270bv5 [1, -1, 0, -4665879, -4899031565] [2] 23068672  
333270.bv1 333270bv6 [1, -1, 0, -79984899, -275314176257] [2] 23068672  

Rank

sage: E.rank()
 

The elliptic curves in class 333270bv have rank \(0\).

Modular form 333270.2.a.bv

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + 4q^{11} - 2q^{13} + q^{14} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.