Properties

Label 4928.x
Number of curves $3$
Conductor $4928$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 4928.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4928.x1 4928t1 \([0, 1, 0, -357, -2719]\) \(-78843215872/539\) \(-34496\) \([]\) \(960\) \(0.051574\) \(\Gamma_0(N)\)-optimal
4928.x2 4928t2 \([0, 1, 0, -197, -4999]\) \(-13278380032/156590819\) \(-10021812416\) \([]\) \(2880\) \(0.60088\)  
4928.x3 4928t3 \([0, 1, 0, 1763, 128281]\) \(9463555063808/115539436859\) \(-7394523958976\) \([]\) \(8640\) \(1.1502\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4928.x have rank \(0\).

Complex multiplication

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

Modular form 4928.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{3} - 3 q^{5} - q^{7} - 2 q^{9} - q^{11} + 4 q^{13} - 3 q^{15} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.