Properties

Label 2800.l
Number of curves $2$
Conductor $2800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 2800.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.l1 2800be2 \([0, -1, 0, -59333, -5570963]\) \(-2887553024/16807\) \(-134456000000000\) \([]\) \(8000\) \(1.5521\)  
2800.l2 2800be1 \([0, -1, 0, 667, 9037]\) \(4096/7\) \(-56000000000\) \([]\) \(1600\) \(0.74734\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2800.l have rank \(0\).

Complex multiplication

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

Modular form 2800.2.a.l

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.