Elliptic curve isogeny class with Cremona label 49818z (LMFDB label 49818.ba)

• Label: 49818z
• Number of curves: $1$
• Conductor: $49818$
• CM: no
• Rank: $1$

Rank

The elliptic curve 49818z1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(19\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 49818z do not have complex multiplication.

Modular form 49818.2.a.z

Elliptic curves in class 49818z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49818.ba1	49818z1	\([1, 1, 1, 40, -871]\)	\(19575719/953856\)	\(-344342016\)	\([]\)	\(25920\)	\(0.31783\)	\(\Gamma_0(N)\)-optimal