Properties

Label 7056.k
Number of curves $6$
Conductor $7056$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7056.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.k1 7056by3 [0, 0, 0, -9483411, -11240741806] [2] 147456  
7056.k2 7056by5 [0, 0, 0, -6449331, 6243532274] [2] 294912  
7056.k3 7056by4 [0, 0, 0, -733971, -85657390] [2, 2] 147456  
7056.k4 7056by2 [0, 0, 0, -592851, -175550830] [2, 2] 73728  
7056.k5 7056by1 [0, 0, 0, -28371, -4061806] [2] 36864 \(\Gamma_0(N)\)-optimal
7056.k6 7056by6 [0, 0, 0, 2723469, -661666894] [2] 294912  

Rank

sage: E.rank()
 

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

Modular form 7056.2.a.k

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 4q^{11} - 6q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.