Properties

Label 6160g
Number of curves 4
Conductor 6160
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6160.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6160g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6160.j3 6160g1 [0, -1, 0, -896, -200704] [2] 13824 \(\Gamma_0(N)\)-optimal
6160.j2 6160g2 [0, -1, 0, -57216, -5201920] [2] 27648  
6160.j4 6160g3 [0, -1, 0, 8064, 5411840] [2] 41472  
6160.j1 6160g4 [0, -1, 0, -417856, 101158656] [2] 82944  

Rank

sage: E.rank()
 

The elliptic curves in class 6160g have rank \(1\).

Modular form 6160.2.a.j

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} - q^{7} + q^{9} + q^{11} - 4q^{13} - 2q^{15} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.