Elliptic curve isogeny class with Cremona label 21443a (LMFDB label 21443.a)

• Label: 21443a
• Number of curves: $1$
• Conductor: $21443$
• CM: no
• Rank: $3$

Rank

The elliptic curve 21443a1 has rank \(3\).

L-function data

Bad L-factors:

Prime	L-Factor
\(41\)	\(1 + T\)
\(523\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 21443a do not have complex multiplication.

Modular form 21443.2.a.a

Elliptic curves in class 21443a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21443.a1	21443a1	\([1, 1, 1, -5, 6]\)	\(-13997521/21443\)	\(-21443\)	\([]\)	\(2912\)	\(-0.47738\)	\(\Gamma_0(N)\)-optimal