Properties

Label 7056.bq
Number of curves $4$
Conductor $7056$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bq1 7056w3 \([0, 0, 0, -1778259, -912726430]\) \(7080974546692/189\) \(16598831993856\) \([2]\) \(73728\) \(2.0504\)  
7056.bq2 7056w4 \([0, 0, 0, -173019, 3322298]\) \(6522128932/3720087\) \(326714810135067648\) \([2]\) \(73728\) \(2.0504\)  
7056.bq3 7056w2 \([0, 0, 0, -111279, -14224210]\) \(6940769488/35721\) \(784294811709696\) \([2, 2]\) \(36864\) \(1.7039\)  
7056.bq4 7056w1 \([0, 0, 0, -3234, -459277]\) \(-2725888/64827\) \(-88959365217072\) \([2]\) \(18432\) \(1.3573\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7056.bq have rank \(1\).

Complex multiplication

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

Modular form 7056.2.a.bq

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.