Properties

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

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

Elliptic curves in class 333270.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.bv1 333270bv6 \([1, -1, 0, -79984899, -275314176257]\) \(524388516989299201/3150\) \(339942213705150\) \([2]\) \(23068672\) \(2.8538\)  
333270.bv2 333270bv4 \([1, -1, 0, -4999149, -4300678607]\) \(128031684631201/9922500\) \(1070817973171222500\) \([2, 2]\) \(11534336\) \(2.5072\)  
333270.bv3 333270bv5 \([1, -1, 0, -4665879, -4899031565]\) \(-104094944089921/35880468750\) \(-3872154277985224218750\) \([2]\) \(23068672\) \(2.8538\)  
333270.bv4 333270bv3 \([1, -1, 0, -1761669, 851066185]\) \(5602762882081/345888060\) \(37327604066850712860\) \([2]\) \(11534336\) \(2.5072\)  
333270.bv5 333270bv2 \([1, -1, 0, -333369, -57618275]\) \(37966934881/8643600\) \(932801434406931600\) \([2, 2]\) \(5767168\) \(2.1607\)  
333270.bv6 333270bv1 \([1, -1, 0, 47511, -5590067]\) \(109902239/188160\) \(-20305881565320960\) \([2]\) \(2883584\) \(1.8141\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 333270.bv do not have complex multiplication.

Modular form 333270.2.a.bv

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.