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Properties

Label 50286.p
Number of curves $2$
Conductor $50286$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 50286.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50286.p1 50286n2 \([1, 1, 1, -1881685, -997191607]\) \(-30526075007211889/103499257854\) \(-2498220477899716926\) \([]\) \(987840\) \(2.3943\)  
50286.p2 50286n1 \([1, 1, 1, -295, 673373]\) \(-117649/8118144\) \(-195952260951936\) \([]\) \(141120\) \(1.4213\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 50286.p have rank \(0\).

Complex multiplication

The elliptic curves in class 50286.p do not have complex multiplication.

Modular form 50286.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + q^{10} + 2 q^{11} - q^{12} - q^{14} - q^{15} + q^{16} + q^{18} - q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.