Elliptic curve isogeny class with LMFDB label 247744.bu (Cremona label 247744bu)

• Label: 247744.bu
• Number of curves: $1$
• Conductor: $247744$
• CM: no
• Rank: $1$

Rank

The elliptic curve 247744.bu1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 247744.bu do not have complex multiplication.

Modular form 247744.2.a.bu

Elliptic curves in class 247744.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
247744.bu1	247744bu1	\([0, 1, 0, -1192, 15406]\)	\(24897088/79\)	\(594833344\)	\([]\)	\(120960\)	\(0.55043\)	\(\Gamma_0(N)\)-optimal