Properties

Label 388080br
Number of curves $4$
Conductor $388080$
CM no
Rank $1$
Graph

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

Elliptic curves in class 388080br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.br3 388080br1 \([0, 0, 0, -31458, -1831277]\) \(2508888064/396165\) \(543640565215440\) \([2]\) \(1179648\) \(1.5502\) \(\Gamma_0(N)\)-optimal
388080.br2 388080br2 \([0, 0, 0, -139503, 18286702]\) \(13674725584/1334025\) \(29290022289158400\) \([2, 2]\) \(2359296\) \(1.8968\)  
388080.br1 388080br3 \([0, 0, 0, -2176923, 1236256378]\) \(12990838708516/144375\) \(12679663328640000\) \([2]\) \(4718592\) \(2.2434\)  
388080.br4 388080br4 \([0, 0, 0, 169197, 87867682]\) \(6099383804/41507235\) \(-3645352488330685440\) \([2]\) \(4718592\) \(2.2434\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388080br have rank \(1\).

Complex multiplication

The elliptic curves in class 388080br do not have complex multiplication.

Modular form 388080.2.a.br

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{11} - 2 q^{13} + 6 q^{17} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.