Properties

Label 4928e
Number of curves $2$
Conductor $4928$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 4928e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4928.g2 4928e1 \([0, 1, 0, 223, 4927]\) \(4657463/41503\) \(-10879762432\) \([2]\) \(3072\) \(0.60713\) \(\Gamma_0(N)\)-optimal
4928.g1 4928e2 \([0, 1, 0, -3297, 66175]\) \(15124197817/1294139\) \(339250774016\) \([2]\) \(6144\) \(0.95370\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4928.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.