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("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.x1 7056br4 \([0, 0, 0, -806295, 278668978]\) \(2640279346000/3087\) \(67778563974912\) \([2]\) \(55296\) \(1.9371\)  
7056.x2 7056br3 \([0, 0, 0, -49980, 4429159]\) \(-10061824000/352947\) \(-484334321737392\) \([2]\) \(27648\) \(1.5905\)  
7056.x3 7056br2 \([0, 0, 0, -12495, 172186]\) \(9826000/5103\) \(112042115958528\) \([2]\) \(18432\) \(1.3878\)  
7056.x4 7056br1 \([0, 0, 0, 2940, 20923]\) \(2048000/1323\) \(-1815497249328\) \([2]\) \(9216\) \(1.0412\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7056.2.a.x

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.