Elliptic curve isogeny class with LMFDB label 49818.u (Cremona label 49818w)

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

Rank

The elliptic curve 49818.u1 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 49818.2.a.u

Elliptic curves in class 49818.u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49818.u1	49818w1	\([1, 1, 1, -9574, 280937]\)	\(5714497/1242\)	\(21093585296922\)	\([]\)	\(164160\)	\(1.2705\)	\(\Gamma_0(N)\)-optimal