Elliptic curve isogeny class with Cremona label 214200bk (LMFDB label 214200.ev)

• Label: 214200bk
• Number of curves: $1$
• Conductor: $214200$
• CM: no
• Rank: $1$

Rank

The elliptic curve 214200bk1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 214200bk do not have complex multiplication.

Modular form 214200.2.a.bk

Elliptic curves in class 214200bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
214200.ev1	214200bk1	\([0, 0, 0, -75, 1195]\)	\(-160000/2023\)	\(-589906800\)	\([]\)	\(87552\)	\(0.36469\)	\(\Gamma_0(N)\)-optimal