Elliptic curve isogeny class with LMFDB label 263442.o (Cremona label 263442o)

• Label: 263442.o
• Number of curves: $1$
• Conductor: $263442$
• CM: no
• Rank: $1$

Rank

The elliptic curve 263442.o1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(23\)	\(1\)
\(83\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 263442.o do not have complex multiplication.

Modular form 263442.2.a.o

Elliptic curves in class 263442.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
263442.o1	263442o1	\([1, 0, 1, -4508, -352726]\)	\(-68417929/322704\)	\(-47771773523856\)	\([]\)	\(1012000\)	\(1.3094\)	\(\Gamma_0(N)\)-optimal