Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bz1 7056bz2 \([0, 0, 0, -5020491, 4351903738]\) \(-16591834777/98304\) \(-82916138081650212864\) \([]\) \(241920\) \(2.6623\)  
7056.bz2 7056bz1 \([0, 0, 0, 165669, 31832458]\) \(596183/864\) \(-728755119858253824\) \([]\) \(80640\) \(2.1130\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7056.2.a.bz

sage: E.q_eigenform(10)
 
\(q + 3q^{5} + 3q^{11} + 4q^{13} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.