Properties

Label 18720.bk
Number of curves $4$
Conductor $18720$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 18720.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18720.bk1 18720bo2 \([0, 0, 0, -230632572, -1348121630464]\) \(454357982636417669333824/3003024375\) \(8966982735360000\) \([2]\) \(1720320\) \(3.1200\)  
18720.bk2 18720bo3 \([0, 0, 0, -15403467, -18008806606]\) \(1082883335268084577352/251301565117746585\) \(93797806577068677358080\) \([2]\) \(1720320\) \(3.1200\)  
18720.bk3 18720bo1 \([0, 0, 0, -14414817, -21063537376]\) \(7099759044484031233216/577161945398025\) \(26928067724490254400\) \([2, 2]\) \(860160\) \(2.7734\) \(\Gamma_0(N)\)-optimal
18720.bk4 18720bo4 \([0, 0, 0, -13430667, -24063029746]\) \(-717825640026599866952/254764560814329735\) \(-95090362794826944929280\) \([4]\) \(1720320\) \(3.1200\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18720.bk have rank \(1\).

Complex multiplication

The elliptic curves in class 18720.bk do not have complex multiplication.

Modular form 18720.2.a.bk

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.