Elliptic curve isogeny class with Cremona label 195195bk (LMFDB label 195195.r)

• Label: 195195bk
• Number of curves: $1$
• Conductor: $195195$
• CM: no
• Rank: $1$

Rank

The elliptic curve 195195bk1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(11\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 195195bk do not have complex multiplication.

Modular form 195195.2.a.bk

Elliptic curves in class 195195bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
195195.r1	195195bk1	\([0, -1, 1, 1309, 66536]\)	\(112818618368/947244375\)	\(-2081095891875\)	\([]\)	\(269568\)	\(1.0450\)	\(\Gamma_0(N)\)-optimal