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

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

Rank

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

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 2800.2.a.a

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 2800a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2800.p4	2800a1	\([0, 0, 0, 25, -250]\)	\(432/7\)	\(-28000000\)	\([2]\)	\(512\)	\(0.10954\)	\(\Gamma_0(N)\)-optimal
2800.p3	2800a2	\([0, 0, 0, -475, -3750]\)	\(740772/49\)	\(784000000\)	\([2, 2]\)	\(1024\)	\(0.45611\)
2800.p1	2800a3	\([0, 0, 0, -7475, -248750]\)	\(1443468546/7\)	\(224000000\)	\([2]\)	\(2048\)	\(0.80269\)
2800.p2	2800a4	\([0, 0, 0, -1475, 17250]\)	\(11090466/2401\)	\(76832000000\)	\([2]\)	\(2048\)	\(0.80269\)