Properties

Label 20184f
Number of curves $6$
Conductor $20184$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20184f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20184.i5 20184f1 \([0, 1, 0, 561, 6510]\) \(2048/3\) \(-28551519408\) \([2]\) \(12096\) \(0.69172\) \(\Gamma_0(N)\)-optimal
20184.i4 20184f2 \([0, 1, 0, -3644, 62016]\) \(35152/9\) \(1370472931584\) \([2, 2]\) \(24192\) \(1.0383\)  
20184.i3 20184f3 \([0, 1, 0, -20464, -1081744]\) \(1556068/81\) \(49337025537024\) \([2, 2]\) \(48384\) \(1.3849\)  
20184.i2 20184f4 \([0, 1, 0, -54104, 4825440]\) \(28756228/3\) \(1827297242112\) \([2]\) \(48384\) \(1.3849\)  
20184.i1 20184f5 \([0, 1, 0, -323224, -70837648]\) \(3065617154/9\) \(10963783452672\) \([2]\) \(96768\) \(1.7314\)  
20184.i6 20184f6 \([0, 1, 0, 13176, -4257360]\) \(207646/6561\) \(-7992598136997888\) \([2]\) \(96768\) \(1.7314\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20184f have rank \(0\).

Complex multiplication

The elliptic curves in class 20184f do not have complex multiplication.

Modular form 20184.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{5} + q^{9} - 4q^{11} - 2q^{13} - 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.