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Properties

Label 2850.x
Number of curves $2$
Conductor $2850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 2850.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2850.x1 2850ba1 \([1, 0, 0, -2388, -45108]\) \(96386901625/18468\) \(288562500\) \([2]\) \(2880\) \(0.62403\) \(\Gamma_0(N)\)-optimal
2850.x2 2850ba2 \([1, 0, 0, -2138, -54858]\) \(-69173457625/42633378\) \(-666146531250\) \([2]\) \(5760\) \(0.97060\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2850.x have rank \(0\).

Complex multiplication

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

Modular form 2850.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 4 q^{7} + q^{8} + q^{9} + 4 q^{11} + q^{12} - 4 q^{14} + q^{16} + 2 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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.