Properties

Label 7056.x
Number of curves 4
Conductor 7056
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7056.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.x1 7056br4 [0, 0, 0, -806295, 278668978] [2] 55296  
7056.x2 7056br3 [0, 0, 0, -49980, 4429159] [2] 27648  
7056.x3 7056br2 [0, 0, 0, -12495, 172186] [2] 18432  
7056.x4 7056br1 [0, 0, 0, 2940, 20923] [2] 9216 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 7056.2.a.x

sage: E.q_eigenform(10)
 
\( q - 6q^{11} - 2q^{13} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.