Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4928.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4928.d1 4928f2 \([0, 1, 0, -15009, -712769]\) \(1426487591593/2156\) \(565182464\) \([2]\) \(6144\) \(0.94741\)  
4928.d2 4928f1 \([0, 1, 0, -929, -11585]\) \(-338608873/13552\) \(-3552575488\) \([2]\) \(3072\) \(0.60083\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4928.2.a.d

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