Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("7056.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.bu1 7056bt2 [0, 0, 0, -399, 2842] [2] 3072  
7056.bu2 7056bt1 [0, 0, 0, -84, -245] [2] 1536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 7056.2.a.bu

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.