Elliptic curve isogeny class with Cremona label 398544o (LMFDB label 398544.o)

• Label: 398544o
• Number of curves: $1$
• Conductor: $398544$
• CM: no
• Rank: $0$

Rank

The elliptic curve 398544o1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(19\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 398544o do not have complex multiplication.

Modular form 398544.2.a.o

Elliptic curves in class 398544o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
398544.o1	398544o1	\([0, -1, 0, -44561, -3606003]\)	\(-5573108202496/385641\)	\(-677148574464\)	\([]\)	\(768000\)	\(1.3238\)	\(\Gamma_0(N)\)-optimal