Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.bo1 7056x3 [0, 0, 0, -131859, -18429390] [2] 24576  
7056.bo2 7056x4 [0, 0, 0, -26019, 1278018] [2] 24576  
7056.bo3 7056x2 [0, 0, 0, -8379, -277830] [2, 2] 12288  
7056.bo4 7056x1 [0, 0, 0, 441, -18522] [2] 6144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7056.2.a.bo

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - 4q^{11} - 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.