Elliptic curve isogeny class with LMFDB label 22491.b (Cremona label 22491w)

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

Rank

The elliptic curve 22491.b1 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 \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 22491.2.a.b

Elliptic curves in class 22491.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
22491.b1	22491w1	\([0, 0, 1, -1911, 32156]\)	\(-242970624/17\)	\(-54000891\)	\([]\)	\(19008\)	\(0.53678\)	\(\Gamma_0(N)\)-optimal