Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2800u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.x2 2800u1 \([0, 1, 0, 72, -172]\) \(397535/392\) \(-40140800\) \([]\) \(576\) \(0.14598\) \(\Gamma_0(N)\)-optimal
2800.x1 2800u2 \([0, 1, 0, -728, 10388]\) \(-417267265/235298\) \(-24094515200\) \([]\) \(1728\) \(0.69528\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2800.2.a.u

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