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Properties

Label 252050d
Number of curves $2$
Conductor $252050$
CM no
Rank $0$
Graph

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

Elliptic curves in class 252050d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
252050.d2 252050d1 \([1, 1, 0, -1010825, -388209875]\) \(57066625/568\) \(1136890019798875000\) \([]\) \(2903040\) \(2.2832\) \(\Gamma_0(N)\)-optimal
252050.d1 252050d2 \([1, 1, 0, -7312075, 7386272375]\) \(21601086625/715822\) \(1432765647451532218750\) \([]\) \(8709120\) \(2.8325\)  

Rank

sage: E.rank()
 

The elliptic curves in class 252050d have rank \(0\).

Complex multiplication

The elliptic curves in class 252050d do not have complex multiplication.

Modular form 252050.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} - 2 q^{9} - q^{12} - q^{13} + q^{14} + q^{16} + 2 q^{18} - q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.