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 j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bo1 7056x3 \([0, 0, 0, -131859, -18429390]\) \(1443468546/7\) \(1229543110656\) \([2]\) \(24576\) \(1.5202\)  
7056.bo2 7056x4 \([0, 0, 0, -26019, 1278018]\) \(11090466/2401\) \(421733286955008\) \([2]\) \(24576\) \(1.5202\)  
7056.bo3 7056x2 \([0, 0, 0, -8379, -277830]\) \(740772/49\) \(4303400887296\) \([2, 2]\) \(12288\) \(1.1737\)  
7056.bo4 7056x1 \([0, 0, 0, 441, -18522]\) \(432/7\) \(-153692888832\) \([2]\) \(6144\) \(0.82708\) \(\Gamma_0(N)\)-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)
 
\(q + 2q^{5} - 4q^{11} - 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})\)  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.