Elliptic curve isogeny class with Cremona label 19133b (LMFDB label 19133.a)

• Label: 19133b
• Number of curves: $1$
• Conductor: $19133$
• CM: no
• Rank: $1$

Rank

The elliptic curve 19133b1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 19133b do not have complex multiplication.

Modular form 19133.2.a.b

Elliptic curves in class 19133b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19133.a1	19133b1	\([0, 0, 1, 22021, 718480]\)	\(25102282752/19266931\)	\(-906429743061211\)	\([]\)	\(99360\)	\(1.5581\)	\(\Gamma_0(N)\)-optimal