Elliptic curve isogeny class with Cremona label 2800w (LMFDB label 2800.e)

• Label: 2800w
• Number of curves: $2$
• Conductor: $2800$
• CM: no
• Rank: $1$

Elliptic curves in class 2800w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2800.e2	2800w1	\([0, 1, 0, 2, 3]\)	\(1280/7\)	\(-2800\)	\([]\)	\(144\)	\(-0.65649\)	\(\Gamma_0(N)\)-optimal
2800.e1	2800w2	\([0, 1, 0, -98, 343]\)	\(-262885120/343\)	\(-137200\)	\([]\)	\(432\)	\(-0.10718\)

Rank

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

Complex multiplication

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

Modular form 2800.2.a.w

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.