Elliptic curve isogeny class with Cremona label 2850f (LMFDB label 2850.f)

• Label: 2850f
• Number of curves: $1$
• Conductor: $2850$
• CM: no
• Rank: $0$

Rank

The elliptic curve 2850f1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2850f do not have complex multiplication.

Modular form 2850.2.a.f

Elliptic curves in class 2850f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2850.f1	2850f1	\([1, 1, 0, -12825, 577125]\)	\(-23891790625/1181952\)	\(-11542500000000\)	\([]\)	\(9600\)	\(1.2678\)	\(\Gamma_0(N)\)-optimal