Elliptic curve isogeny class with LMFDB label 291023.f (Cremona label 291023f)

• Label: 291023.f
• Number of curves: $1$
• Conductor: $291023$
• CM: no
• Rank: $1$

Rank

The elliptic curve 291023.f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(17\)	\(1\)
\(19\)	\(1 + T\)
\(53\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 291023.f do not have complex multiplication.

Modular form 291023.2.a.f

Elliptic curves in class 291023.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
291023.f1	291023f1	\([0, 0, 1, 17629, -514637]\)	\(25102282752/19266931\)	\(-465056876430739\)	\([]\)	\(1391040\)	\(1.5025\)	\(\Gamma_0(N)\)-optimal