Properties

Label 179520.fi
Number of curves 6
Conductor 179520
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("179520.fi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 179520.fi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179520.fi1 179520ga6 [0, 1, 0, -18696961, -31120025761] [2] 9437184  
179520.fi2 179520ga4 [0, 1, 0, -1272961, -394544161] [2, 2] 4718592  
179520.fi3 179520ga2 [0, 1, 0, -472961, 120175839] [2, 2] 2359296  
179520.fi4 179520ga1 [0, 1, 0, -467841, 123011295] [2] 1179648 \(\Gamma_0(N)\)-optimal
179520.fi5 179520ga3 [0, 1, 0, 245119, 453508575] [2] 4718592  
179520.fi6 179520ga5 [0, 1, 0, 3351039, -2598342561] [4] 9437184  

Rank

sage: E.rank()
 

The elliptic curves in class 179520.fi have rank \(2\).

Modular form 179520.2.a.fi

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{9} + q^{11} - 6q^{13} - q^{15} + q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.