Properties

Label 2800.p
Number of curves $4$
Conductor $2800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2800.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2800.p1 2800a3 [0, 0, 0, -7475, -248750] [2] 2048  
2800.p2 2800a4 [0, 0, 0, -1475, 17250] [2] 2048  
2800.p3 2800a2 [0, 0, 0, -475, -3750] [2, 2] 1024  
2800.p4 2800a1 [0, 0, 0, 25, -250] [2] 512 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2800.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{7} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20}) \)

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.