Elliptic curve isogeny class with Cremona label 193550bf (LMFDB label 193550.cz)

• Label: 193550bf
• Number of curves: $1$
• Conductor: $193550$
• CM: no
• Rank: $1$

Rank

The elliptic curve 193550bf1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(79\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 193550bf do not have complex multiplication.

Modular form 193550.2.a.bf

Elliptic curves in class 193550bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
193550.cz1	193550bf1	\([1, 0, 0, -1328118, 590297252]\)	\(-42298759185902121413/107219563577344\)	\(-656719826911232000\)	\([]\)	\(3074688\)	\(2.2957\)	\(\Gamma_0(N)\)-optimal