Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("7056.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.p1 7056bx5 [0, 0, 0, -5532051, 5008150546] [2] 98304  
7056.p2 7056bx4 [0, 0, 0, -345891, 78186850] [2, 2] 49152  
7056.p3 7056bx3 [0, 0, 0, -275331, -55270334] [2] 49152  
7056.p4 7056bx6 [0, 0, 0, -240051, 126936754] [2] 98304  
7056.p5 7056bx2 [0, 0, 0, -28371, 394450] [2, 2] 24576  
7056.p6 7056bx1 [0, 0, 0, 6909, 48706] [2] 12288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 7056.2.a.p

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.