Elliptic curve isogeny class with LMFDB label 850.f (Cremona label 850j)

• Label: 850.f
• Number of curves: $1$
• Conductor: $850$
• CM: no
• Rank: $0$

Rank

The elliptic curve 850.f1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 850.f do not have complex multiplication.

Modular form 850.2.a.f

Elliptic curves in class 850.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
850.f1	850j1	\([1, -1, 1, -255, -1503]\)	\(-116930169/170\)	\(-2656250\)	\([]\)	\(480\)	\(0.13475\)	\(\Gamma_0(N)\)-optimal