Properties

Label 7056.br
Number of curves $4$
Conductor $7056$
CM no
Rank $1$
Graph

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

Elliptic curves in class 7056.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.br1 7056v3 \([0, 0, 0, -67179, -6693302]\) \(381775972/567\) \(49796495981568\) \([2]\) \(24576\) \(1.5292\)  
7056.br2 7056v2 \([0, 0, 0, -5439, -37730]\) \(810448/441\) \(9682651996416\) \([2, 2]\) \(12288\) \(1.1826\)  
7056.br3 7056v1 \([0, 0, 0, -3234, 70315]\) \(2725888/21\) \(28817416656\) \([2]\) \(6144\) \(0.83607\) \(\Gamma_0(N)\)-optimal
7056.br4 7056v4 \([0, 0, 0, 21021, -297038]\) \(11696828/7203\) \(-632599930432512\) \([2]\) \(24576\) \(1.5292\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7056.br have rank \(1\).

Complex multiplication

The elliptic curves in class 7056.br do not have complex multiplication.

Modular form 7056.2.a.br

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.