Properties

Label 172480.gf
Number of curves 4
Conductor 172480
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("172480.gf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 172480.gf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
172480.gf1 172480du4 [0, -1, 0, -81899841, -277169852959] [2] 31850496  
172480.gf2 172480du2 [0, -1, 0, -11214401, 14330140385] [2] 10616832  
172480.gf3 172480du1 [0, -1, 0, -175681, 551610081] [2] 5308416 \(\Gamma_0(N)\)-optimal
172480.gf4 172480du3 [0, -1, 0, 1580479, -14857991455] [2] 15925248  

Rank

sage: E.rank()
 

The elliptic curves in class 172480.gf have rank \(1\).

Modular form 172480.2.a.gf

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.