Properties

Label 2304.o
Number of curves $4$
Conductor $2304$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 2304.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2304.o1 2304f4 \([0, 0, 0, -23304, 1369280]\) \(58591911104/243\) \(5804752896\) \([2]\) \(2560\) \(1.0829\)  
2304.o2 2304f3 \([0, 0, 0, -1434, 22088]\) \(-873722816/59049\) \(-22039921152\) \([2]\) \(1280\) \(0.73631\)  
2304.o3 2304f2 \([0, 0, 0, -264, -1600]\) \(85184/3\) \(71663616\) \([2]\) \(512\) \(0.27816\)  
2304.o4 2304f1 \([0, 0, 0, 6, -88]\) \(64/9\) \(-3359232\) \([2]\) \(256\) \(-0.068409\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2304.o have rank \(0\).

Complex multiplication

The elliptic curves in class 2304.o do not have complex multiplication.

Modular form 2304.2.a.o

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + 2 q^{7} - 4 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.