Properties

Label 20160.y
Number of curves $4$
Conductor $20160$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 20160.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.y1 20160cs4 \([0, 0, 0, -15228, 289872]\) \(1210991472/588245\) \(189700937072640\) \([2]\) \(55296\) \(1.4332\)  
20160.y2 20160cs3 \([0, 0, 0, -12528, 539352]\) \(10788913152/8575\) \(172832486400\) \([2]\) \(27648\) \(1.0866\)  
20160.y3 20160cs2 \([0, 0, 0, -8028, -276848]\) \(129348709488/6125\) \(2709504000\) \([2]\) \(18432\) \(0.88389\)  
20160.y4 20160cs1 \([0, 0, 0, -528, -3848]\) \(588791808/109375\) \(3024000000\) \([2]\) \(9216\) \(0.53732\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20160.y have rank \(0\).

Complex multiplication

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

Modular form 20160.2.a.y

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