Properties

Label 20400dk
Number of curves $4$
Conductor $20400$
CM no
Rank $0$
Graph

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

Elliptic curves in class 20400dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20400.dp2 20400dk1 \([0, 1, 0, -102208, -12606412]\) \(1845026709625/793152\) \(50761728000000\) \([2]\) \(82944\) \(1.5900\) \(\Gamma_0(N)\)-optimal
20400.dp3 20400dk2 \([0, 1, 0, -86208, -16670412]\) \(-1107111813625/1228691592\) \(-78636261888000000\) \([2]\) \(165888\) \(1.9366\)  
20400.dp1 20400dk3 \([0, 1, 0, -300208, 47765588]\) \(46753267515625/11591221248\) \(741838159872000000\) \([2]\) \(248832\) \(2.1393\)  
20400.dp4 20400dk4 \([0, 1, 0, 723792, 303765588]\) \(655215969476375/1001033261568\) \(-64066128740352000000\) \([2]\) \(497664\) \(2.4859\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20400dk have rank \(0\).

Complex multiplication

The elliptic curves in class 20400dk do not have complex multiplication.

Modular form 20400.2.a.dk

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{7} + q^{9} - 2 q^{13} + q^{17} + 4 q^{19} + O(q^{20})\) 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 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.