Elliptic curve isogeny class with LMFDB label 5200.r (Cremona label 5200n)

• Label: 5200.r
• Number of curves: $4$
• Conductor: $5200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 5200.r have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5200.r do not have complex multiplication.

Modular form 5200.2.a.r

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 5200.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5200.r1	5200n3	\([0, 0, 0, -554675, 159003250]\)	\(294889639316481/260\)	\(16640000000\)	\([2]\)	\(18432\)	\(1.6937\)
5200.r2	5200n2	\([0, 0, 0, -34675, 2483250]\)	\(72043225281/67600\)	\(4326400000000\)	\([2, 2]\)	\(9216\)	\(1.3471\)
5200.r3	5200n4	\([0, 0, 0, -26675, 3659250]\)	\(-32798729601/71402500\)	\(-4569760000000000\)	\([2]\)	\(18432\)	\(1.6937\)
5200.r4	5200n1	\([0, 0, 0, -2675, 19250]\)	\(33076161/16640\)	\(1064960000000\)	\([2]\)	\(4608\)	\(1.0005\)	\(\Gamma_0(N)\)-optimal