Properties

Label 254100br
Number of curves $4$
Conductor $254100$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 254100br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254100.br3 254100br1 \([0, -1, 0, -8050533, -8919520938]\) \(-130287139815424/2250652635\) \(-996792108178308750000\) \([2]\) \(14929920\) \(2.8272\) \(\Gamma_0(N)\)-optimal
254100.br2 254100br2 \([0, -1, 0, -129337908, -566113721688]\) \(33766427105425744/9823275\) \(69610123529100000000\) \([2]\) \(29859840\) \(3.1738\)  
254100.br4 254100br3 \([0, -1, 0, 31153467, -42767274438]\) \(7549996227362816/6152409907875\) \(-2724842362201235718750000\) \([2]\) \(44789760\) \(3.3765\)  
254100.br1 254100br4 \([0, -1, 0, -150028908, -372881561688]\) \(52702650535889104/22020583921875\) \(156043230692883187500000000\) \([2]\) \(89579520\) \(3.7231\)  

Rank

sage: E.rank()
 

The elliptic curves in class 254100br have rank \(0\).

Complex multiplication

The elliptic curves in class 254100br do not have complex multiplication.

Modular form 254100.2.a.br

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.