Elliptic curve isogeny class with Cremona label 398400ix (LMFDB label 398400.ix)

• Label: 398400ix
• Number of curves: $1$
• Conductor: $398400$
• CM: no
• Rank: $1$

Rank

The elliptic curve 398400ix1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(83\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	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
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 398400ix do not have complex multiplication.

Modular form 398400.2.a.ix

Elliptic curves in class 398400ix

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
398400.ix1	398400ix1	\([0, 1, 0, -13633, 1848863]\)	\(-68417929/322704\)	\(-1321795584000000\)	\([]\)	\(2150400\)	\(1.5861\)	\(\Gamma_0(N)\)-optimal