Properties

Label 2800.m
Number of curves $4$
Conductor $2800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2800.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2800.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2800.m1 2800o4 [0, 0, 0, -107075, 13485250] [2] 9216  
2800.m2 2800o3 [0, 0, 0, -35075, -2362750] [2] 9216  
2800.m3 2800o2 [0, 0, 0, -7075, 185250] [2, 2] 4608  
2800.m4 2800o1 [0, 0, 0, 925, 17250] [2] 2304 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 2800.2.a.m

sage: E.q_eigenform(10)
 
\( q - q^{7} - 3q^{9} - 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.