Elliptic curve isogeny class with Cremona label 49343c (LMFDB label 49343.c)

• Label: 49343c
• Number of curves: $1$
• Conductor: $49343$
• CM: no
• Rank: $1$

Rank

The elliptic curve 49343c1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(7\)	\(1\)
\(19\)	\(1 - T\)
\(53\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 49343c do not have complex multiplication.

Modular form 49343.2.a.c

Elliptic curves in class 49343c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49343.c1	49343c1	\([0, 0, 1, 2989, 35929]\)	\(25102282752/19266931\)	\(-2266735165219\)	\([]\)	\(104328\)	\(1.0589\)	\(\Gamma_0(N)\)-optimal