Elliptic curve isogeny class with Cremona label 11197a (LMFDB label 11197.a)

• Label: 11197a
• Number of curves: $1$
• Conductor: $11197$
• CM: no
• Rank: $3$

Rank

The elliptic curve 11197a1 has rank \(3\).

L-function data

Bad L-factors:

Prime	L-Factor
\(11197\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11197a do not have complex multiplication.

Modular form 11197.2.a.a

Elliptic curves in class 11197a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11197.a1	11197a1	\([1, -1, 1, -6, 0]\)	\(20346417/11197\)	\(11197\)	\([]\)	\(2080\)	\(-0.53244\)	\(\Gamma_0(N)\)-optimal