Properties

Label 28050.r
Number of curves $2$
Conductor $28050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 28050.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28050.r1 28050m1 [1, 1, 0, -4900, -134000] [2] 30720 \(\Gamma_0(N)\)-optimal
28050.r2 28050m2 [1, 1, 0, -3900, -189000] [2] 61440  

Rank

sage: E.rank()
 

The elliptic curves in class 28050.r have rank \(1\).

Complex multiplication

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

Modular form 28050.2.a.r

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 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.