Elliptic curve isogeny class with Cremona label 858f (LMFDB label 858.e)

• Label: 858f
• Number of curves: $1$
• Conductor: $858$
• CM: no
• Rank: $1$

Rank

The elliptic curve 858f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 858f do not have complex multiplication.

Modular form 858.2.a.f

Elliptic curves in class 858f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
858.e1	858f1	\([1, 1, 1, -572, 118685]\)	\(-20699471212993/6097712265216\)	\(-6097712265216\)	\([]\)	\(2640\)	\(1.1324\)	\(\Gamma_0(N)\)-optimal