Elliptic curve isogeny class with Cremona label 22491k (LMFDB label 22491.s)

• Label: 22491k
• Number of curves: $1$
• Conductor: $22491$
• CM: no
• Rank: $1$

Rank

The elliptic curve 22491k1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 22491k do not have complex multiplication.

Modular form 22491.2.a.k

Elliptic curves in class 22491k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
22491.s1	22491k1	\([0, 0, 1, 22344, 1718001]\)	\(43153096704/69572993\)	\(-1989001911990051\)	\([]\)	\(80640\)	\(1.6207\)	\(\Gamma_0(N)\)-optimal