Properties

Label 4928.o
Number of curves $4$
Conductor $4928$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4928.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4928.o1 4928bb4 \([0, 0, 0, -330476, 73123664]\) \(15226621995131793/2324168\) \(609266696192\) \([4]\) \(18432\) \(1.6669\)  
4928.o2 4928bb3 \([0, 0, 0, -38636, -1122480]\) \(24331017010833/12004097336\) \(3146802092048384\) \([2]\) \(18432\) \(1.6669\)  
4928.o3 4928bb2 \([0, 0, 0, -20716, 1135440]\) \(3750606459153/45914176\) \(12036125753344\) \([2, 2]\) \(9216\) \(1.3203\)  
4928.o4 4928bb1 \([0, 0, 0, -236, 45904]\) \(-5545233/3469312\) \(-909459324928\) \([2]\) \(4608\) \(0.97375\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4928.o have rank \(1\).

Complex multiplication

The elliptic curves in class 4928.o do not have complex multiplication.

Modular form 4928.2.a.o

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} - 3 q^{9} - q^{11} - 2 q^{13} + 2 q^{17} + O(q^{20})\) 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 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.