Properties

Label 20160t
Number of curves $4$
Conductor $20160$
CM no
Rank $1$
Graph

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

Elliptic curves in class 20160t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.er2 20160t1 \([0, 0, 0, -6732, 212336]\) \(4767078987/6860\) \(48554311680\) \([2]\) \(18432\) \(0.95293\) \(\Gamma_0(N)\)-optimal
20160.er3 20160t2 \([0, 0, 0, -4812, 335984]\) \(-1740992427/5882450\) \(-41635322265600\) \([2]\) \(36864\) \(1.2995\)  
20160.er1 20160t3 \([0, 0, 0, -26892, -1487376]\) \(416832723/56000\) \(288947699712000\) \([2]\) \(55296\) \(1.5022\)  
20160.er4 20160t4 \([0, 0, 0, 42228, -7874064]\) \(1613964717/6125000\) \(-31603654656000000\) \([2]\) \(110592\) \(1.8488\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 20160t do not have complex multiplication.

Modular form 20160.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} - 2 q^{13} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.