Properties

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

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

Elliptic curves in class 7056.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.p1 7056bx5 \([0, 0, 0, -5532051, 5008150546]\) \(53297461115137/147\) \(51640810647552\) \([2]\) \(98304\) \(2.2896\)  
7056.p2 7056bx4 \([0, 0, 0, -345891, 78186850]\) \(13027640977/21609\) \(7591199165190144\) \([2, 2]\) \(49152\) \(1.9430\)  
7056.p3 7056bx3 \([0, 0, 0, -275331, -55270334]\) \(6570725617/45927\) \(16134064698028032\) \([2]\) \(49152\) \(1.9430\)  
7056.p4 7056bx6 \([0, 0, 0, -240051, 126936754]\) \(-4354703137/17294403\) \(-6075489731873845248\) \([2]\) \(98304\) \(2.2896\)  
7056.p5 7056bx2 \([0, 0, 0, -28371, 394450]\) \(7189057/3969\) \(1394301887483904\) \([2, 2]\) \(24576\) \(1.5965\)  
7056.p6 7056bx1 \([0, 0, 0, 6909, 48706]\) \(103823/63\) \(-22131775991808\) \([2]\) \(12288\) \(1.2499\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7056.2.a.p

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.