Properties

Label 2800.y
Number of curves $2$
Conductor $2800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2800.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.y1 2800t2 \([0, 1, 0, -20133, 1092863]\) \(-225637236736/1715\) \(-6860000000\) \([]\) \(3456\) \(1.0623\)  
2800.y2 2800t1 \([0, 1, 0, -133, 2863]\) \(-65536/875\) \(-3500000000\) \([]\) \(1152\) \(0.51296\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2800.y have rank \(1\).

Complex multiplication

The elliptic curves in class 2800.y do not have complex multiplication.

Modular form 2800.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} - 2q^{9} - 3q^{11} + q^{13} + 3q^{17} - 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.