Elliptic curve isogeny class with Cremona label 121847f (LMFDB label 121847.a)

• Label: 121847f
• Number of curves: $1$
• Conductor: $121847$
• CM: no
• Rank: $1$

Rank

The elliptic curve 121847f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(11\)	\(1\)
\(19\)	\(1 - T\)
\(53\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 121847f do not have complex multiplication.

Modular form 121847.2.a.f

Elliptic curves in class 121847f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121847.a1	121847f1	\([0, 0, 1, 7381, 139422]\)	\(25102282752/19266931\)	\(-34132543549291\)	\([]\)	\(372600\)	\(1.2849\)	\(\Gamma_0(N)\)-optimal