Elliptic curve isogeny class with LMFDB label 227154.w (Cremona label 227154f)

• Label: 227154.w
• Number of curves: $1$
• Conductor: $227154$
• CM: no
• Rank: $1$

Rank

The elliptic curve 227154.w1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(17\)	\(1\)
\(131\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 227154.w do not have complex multiplication.

Modular form 227154.2.a.w

Elliptic curves in class 227154.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
227154.w1	227154f1	\([1, 0, 0, 2884, 34728]\)	\(109902239/84888\)	\(-2048989957272\)	\([]\)	\(737280\)	\(1.0504\)	\(\Gamma_0(N)\)-optimal