Elliptic curve isogeny class with LMFDB label 227136.hr (Cremona label 227136bn)

• Label: 227136.hr
• Number of curves: $1$
• Conductor: $227136$
• CM: no
• Rank: $1$

Rank

The elliptic curve 227136.hr1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 227136.hr do not have complex multiplication.

Modular form 227136.2.a.hr

Elliptic curves in class 227136.hr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
227136.hr1	227136bn1	\([0, 1, 0, 1716815, 2782489997]\)	\(1811564780171264/11870974573731\)	\(-3667131322320381080256\)	\([]\)	\(9031680\)	\(2.8196\)	\(\Gamma_0(N)\)-optimal