Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 4928.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4928.r1 4928ba2 \([0, 0, 0, -1420, -5616]\) \(2415899250/1294139\) \(169625387008\) \([2]\) \(3072\) \(0.84596\)  
4928.r2 4928ba1 \([0, 0, 0, 340, -688]\) \(66325500/41503\) \(-2719940608\) \([2]\) \(1536\) \(0.49939\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4928.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.