Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("7056.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.w1 7056bk2 [0, 0, 0, -995043, -396371486] [] 112896  
7056.w2 7056bk1 [0, 0, 0, -7203, 542626] [] 16128 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 7056.2.a.w

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

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.