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

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

Rank

The elliptic curve 19133.a1 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 \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 19133.2.a.a

Elliptic curves in class 19133.a

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