Properties

Label 350064.br
Number of curves $4$
Conductor $350064$
CM no
Rank $1$
Graph

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

Elliptic curves in class 350064.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.br1 350064br3 \([0, 0, 0, -474511755, -3977821865158]\) \(3957101249824708884951625/772310238681366528\) \(2306106015738741550743552\) \([2]\) \(87588864\) \(3.6745\)  
350064.br2 350064br4 \([0, 0, 0, -424376715, -4851184288966]\) \(-2830680648734534916567625/1766676274677722124288\) \(-5275267089367283419569979392\) \([2]\) \(175177728\) \(4.0211\)  
350064.br3 350064br1 \([0, 0, 0, -14446875, 13685927114]\) \(111675519439697265625/37528570137307392\) \(112059709972877675593728\) \([2]\) \(29196288\) \(3.1252\) \(\Gamma_0(N)\)-optimal
350064.br4 350064br2 \([0, 0, 0, 42150885, 94586765258]\) \(2773679829880629422375/2899504554614368272\) \(-8657874208005629830299648\) \([2]\) \(58392576\) \(3.4718\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350064.br have rank \(1\).

Complex multiplication

The elliptic curves in class 350064.br do not have complex multiplication.

Modular form 350064.2.a.br

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