Properties

Label 20160.dc
Number of curves $6$
Conductor $20160$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dc1")
 
E.isogeny_class()
 

Elliptic curves in class 20160.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.dc1 20160ew5 \([0, 0, 0, -878412, -316803184]\) \(784478485879202/221484375\) \(21163161600000000\) \([2]\) \(262144\) \(2.1136\)  
20160.dc2 20160ew3 \([0, 0, 0, -61932, -3601456]\) \(549871953124/200930625\) \(9599610101760000\) \([2, 2]\) \(131072\) \(1.7671\)  
20160.dc3 20160ew2 \([0, 0, 0, -26652, 1634096]\) \(175293437776/4862025\) \(58071715430400\) \([2, 2]\) \(65536\) \(1.4205\)  
20160.dc4 20160ew1 \([0, 0, 0, -26472, 1657784]\) \(2748251600896/2205\) \(1646023680\) \([2]\) \(32768\) \(1.0739\) \(\Gamma_0(N)\)-optimal
20160.dc5 20160ew4 \([0, 0, 0, 5748, 5353616]\) \(439608956/259416045\) \(-12393794555412480\) \([2]\) \(131072\) \(1.7671\)  
20160.dc6 20160ew6 \([0, 0, 0, 190068, -25475056]\) \(7947184069438/7533176175\) \(-719806192887398400\) \([2]\) \(262144\) \(2.1136\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 20160.2.a.dc

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 4 q^{11} + 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.