Properties

Label 7056.bx
Number of curves $2$
Conductor $7056$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 7056.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bx1 7056bi1 \([0, 0, 0, -1491, 22162]\) \(-67645179/8\) \(-43352064\) \([]\) \(3456\) \(0.49093\) \(\Gamma_0(N)\)-optimal
7056.bx2 7056bi2 \([0, 0, 0, 189, 68418]\) \(189/512\) \(-2022633897984\) \([]\) \(10368\) \(1.0402\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7056.2.a.bx

sage: E.q_eigenform(10)
 
\(q + 3 q^{5} - 3 q^{11} - 2 q^{13} + 6 q^{17} + 2 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.