Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("20160.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.t1 20160dr7 [0, 0, 0, -3715788, 1734477712] [2] 884736  
20160.t2 20160dr4 [0, 0, 0, -3318348, 2326649488] [2] 294912  
20160.t3 20160dr6 [0, 0, 0, -1555788, -727058288] [2, 2] 442368  
20160.t4 20160dr3 [0, 0, 0, -1544268, -738638192] [2] 221184  
20160.t5 20160dr2 [0, 0, 0, -207948, 36150928] [2, 2] 147456  
20160.t6 20160dr5 [0, 0, 0, -46668, 90792592] [2] 294912  
20160.t7 20160dr1 [0, 0, 0, -23628, -491888] [2] 73728 \(\Gamma_0(N)\)-optimal
20160.t8 20160dr8 [0, 0, 0, 419892, -2447480432] [2] 884736  

Rank

sage: E.rank()
 

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

Modular form 20160.2.a.t

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.