Elliptic curve isogeny class with LMFDB label 2800.p (Cremona label 2800a)

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

Elliptic curves in class 2800.p

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

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

Isogeny 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

The vertices are labelled with LMFDB labels.