Properties

Label 7056.bg
Number of curves 4
Conductor 7056
CM -7
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7056.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.bg1 7056bq4 [0, 0, 0, -262395, 51731946] [2] 28672  
7056.bg2 7056bq3 [0, 0, 0, -15435, 907578] [2] 14336  
7056.bg3 7056bq2 [0, 0, 0, -5355, -150822] [2] 4096  
7056.bg4 7056bq1 [0, 0, 0, -315, -2646] [2] 2048 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7056.bg have rank \(0\).

Modular form 7056.2.a.bg

sage: E.q_eigenform(10)
 
\( q + 4q^{11} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.