Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bt1 7056g2 \([0, 0, 0, -5439, 154350]\) \(21882096/7\) \(5692329216\) \([2]\) \(6144\) \(0.84666\)  
7056.bt2 7056g1 \([0, 0, 0, -294, 3087]\) \(-55296/49\) \(-2490394032\) \([2]\) \(3072\) \(0.50008\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7056.2.a.bt

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.