Elliptic curve isogeny class with LMFDB label 297.b (Cremona label 297b)

• Label: 297.b
• Number of curves: $1$
• Conductor: $297$
• CM: no
• Rank: $1$

Rank

The elliptic curve 297.b1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 297.b do not have complex multiplication.

Modular form 297.2.a.b

Elliptic curves in class 297.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
297.b1	297b1	\([1, -1, 1, 1, 0]\)	\(9261/11\)	\(-297\)	\([]\)	\(12\)	\(-0.83928\)	\(\Gamma_0(N)\)-optimal