Properties

Label 20160.fh
Number of curves 8
Conductor 20160
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("20160.fh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160.fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.fh1 20160ff7 [0, 0, 0, -1106380812, -14164624511984] [2] 3145728  
20160.fh2 20160ff5 [0, 0, 0, -69148812, -221322182384] [2, 2] 1572864  
20160.fh3 20160ff8 [0, 0, 0, -68716812, -224224012784] [4] 3145728  
20160.fh4 20160ff4 [0, 0, 0, -8680332, 9840860944] [2] 786432  
20160.fh5 20160ff3 [0, 0, 0, -4348812, -3412742384] [2, 2] 786432  
20160.fh6 20160ff2 [0, 0, 0, -616332, 109225744] [2, 2] 393216  
20160.fh7 20160ff1 [0, 0, 0, 120948, 12199696] [2] 196608 \(\Gamma_0(N)\)-optimal
20160.fh8 20160ff6 [0, 0, 0, 731508, -10909262576] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 20160.fh have rank \(1\).

Modular form 20160.2.a.fh

sage: E.q_eigenform(10)
 
\( q + q^{5} + q^{7} + 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.