Elliptic curve isogeny class with LMFDB label 223440.fn (Cremona label 223440d)

• Label: 223440.fn
• Number of curves: $1$
• Conductor: $223440$
• CM: no
• Rank: $0$

Rank

The elliptic curve 223440.fn1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 223440.fn do not have complex multiplication.

Modular form 223440.2.a.fn

Elliptic curves in class 223440.fn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
223440.fn1	223440d1	\([0, 1, 0, -59134481956440, -175089732594702786540]\)	\(-138357846491853121383730987168838623/55816105091607428996184145920\)	\(-9225753268786893570016950370657621770240\)	\([]\)	\(22983367680\)	\(6.6319\)	\(\Gamma_0(N)\)-optimal