Elliptic curve isogeny class with Cremona label 49686u (LMFDB label 49686.j)

• Label: 49686u
• Number of curves: $1$
• Conductor: $49686$
• CM: no
• Rank: $1$

Rank

The elliptic curve 49686u1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 49686u do not have complex multiplication.

Modular form 49686.2.a.u

Elliptic curves in class 49686u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49686.j1	49686u1	\([1, 1, 0, -384081233, -3135674078571]\)	\(-5022437771811277/497757560832\)	\(-621006686647022613654872064\)	\([]\)	\(25698816\)	\(3.8817\)	\(\Gamma_0(N)\)-optimal