Properties

Label 20160.dk
Number of curves $8$
Conductor $20160$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dk1")
 
E.isogeny_class()
 

Elliptic curves in class 20160.dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.dk1 20160en7 \([0, 0, 0, -202309932, -1107576977456]\) \(4791901410190533590281/41160000\) \(7865798492160000\) \([2]\) \(1769472\) \(3.0913\)  
20160.dk2 20160en6 \([0, 0, 0, -12644652, -17305081904]\) \(1169975873419524361/108425318400\) \(20720401019987558400\) \([2, 2]\) \(884736\) \(2.7447\)  
20160.dk3 20160en8 \([0, 0, 0, -11723052, -19934591024]\) \(-932348627918877961/358766164249920\) \(-68561281676264519761920\) \([2]\) \(1769472\) \(3.0913\)  
20160.dk4 20160en4 \([0, 0, 0, -2509932, -1503617456]\) \(9150443179640281/184570312500\) \(35271936000000000000\) \([2]\) \(589824\) \(2.5420\)  
20160.dk5 20160en3 \([0, 0, 0, -848172, -228497456]\) \(353108405631241/86318776320\) \(16495775039430328320\) \([2]\) \(442368\) \(2.3981\)  
20160.dk6 20160en2 \([0, 0, 0, -332652, 38767696]\) \(21302308926361/8930250000\) \(1706597351424000000\) \([2, 2]\) \(294912\) \(2.1954\)  
20160.dk7 20160en1 \([0, 0, 0, -286572, 59024464]\) \(13619385906841/6048000\) \(1155790798848000\) \([2]\) \(147456\) \(1.8488\) \(\Gamma_0(N)\)-optimal
20160.dk8 20160en5 \([0, 0, 0, 1107348, 284719696]\) \(785793873833639/637994920500\) \(-121922727980433408000\) \([2]\) \(589824\) \(2.5420\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 20160.2.a.dk

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 2 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.