Elliptic curve isogeny class with LMFDB label 4200.r (Cremona label 4200y)

• Label: 4200.r
• Number of curves: $1$
• Conductor: $4200$
• CM: no
• Rank: $1$

Rank

The elliptic curve 4200.r1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4200.r do not have complex multiplication.

Modular form 4200.2.a.r

Elliptic curves in class 4200.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4200.r1	4200y1	\([0, 1, 0, -28, 53]\)	\(-6288640/567\)	\(-226800\)	\([]\)	\(384\)	\(-0.22916\)	\(\Gamma_0(N)\)-optimal