Properties

Label 23184bz
Number of curves $4$
Conductor $23184$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 23184bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23184.bt4 23184bz1 \([0, 0, 0, -86259, -15906382]\) \(-23771111713777/22848457968\) \(-68225129917120512\) \([2]\) \(184320\) \(1.9263\) \(\Gamma_0(N)\)-optimal
23184.bt3 23184bz2 \([0, 0, 0, -1609779, -785893390]\) \(154502321244119857/55101928644\) \(164533477300125696\) \([2, 2]\) \(368640\) \(2.2729\)  
23184.bt2 23184bz3 \([0, 0, 0, -1841619, -544733422]\) \(231331938231569617/90942310746882\) \(271552284813217701888\) \([2]\) \(737280\) \(2.6194\)  
23184.bt1 23184bz4 \([0, 0, 0, -25754259, -50306221870]\) \(632678989847546725777/80515134\) \(240416901881856\) \([2]\) \(737280\) \(2.6194\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23184bz have rank \(1\).

Complex multiplication

The elliptic curves in class 23184bz do not have complex multiplication.

Modular form 23184.2.a.bz

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.