Properties

Label 7056.j
Number of curves $2$
Conductor $7056$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.j1 7056j1 \([0, 0, 0, -2646, -46305]\) \(55296/7\) \(259356749904\) \([2]\) \(9216\) \(0.91934\) \(\Gamma_0(N)\)-optimal
7056.j2 7056j2 \([0, 0, 0, 3969, -240786]\) \(11664/49\) \(-29047955989248\) \([2]\) \(18432\) \(1.2659\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7056.2.a.j

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.