Properties

Label 28050dg
Number of curves $2$
Conductor $28050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28050dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28050.dn2 28050dg1 [1, 0, 0, 662, 5792] [2] 24576 \(\Gamma_0(N)\)-optimal
28050.dn1 28050dg2 [1, 0, 0, -3588, 52542] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 28050dg have rank \(0\).

Complex multiplication

The elliptic curves in class 28050dg do not have complex multiplication.

Modular form 28050.2.a.dg

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} + q^{8} + q^{9} + q^{11} + q^{12} + 2q^{14} + q^{16} - q^{17} + q^{18} + O(q^{20}) \)

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.