Elliptic curve isogeny class with LMFDB label 89232.by (Cremona label 89232cl)

• Label: 89232.by
• Number of curves: $1$
• Conductor: $89232$
• CM: no
• Rank: $0$

Rank

The elliptic curve 89232.by1 has rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 89232.by do not have complex multiplication.

Modular form 89232.2.a.by

Elliptic curves in class 89232.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
89232.by1	89232cl1	\([0, 1, 0, -11803016, -14531262732]\)	\(54424690756969/4209228936\)	\(14064014765331836338176\)	\([]\)	\(5660928\)	\(2.9942\)	\(\Gamma_0(N)\)-optimal