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Properties

Label 2850.k
Number of curves $2$
Conductor $2850$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 2850.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2850.k1 2850n2 \([1, 0, 1, -786, 4318]\) \(428831641421/181752822\) \(22719102750\) \([2]\) \(2688\) \(0.68394\)  
2850.k2 2850n1 \([1, 0, 1, 164, 518]\) \(3936827539/3158028\) \(-394753500\) \([2]\) \(1344\) \(0.33736\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2850.k have rank \(1\).

Complex multiplication

The elliptic curves in class 2850.k do not have complex multiplication.

Modular form 2850.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - 4 q^{11} + q^{12} + 4 q^{13} + q^{16} - 6 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.