Elliptic curve isogeny class with LMFDB label 55275.j (Cremona label 55275r)

• Label: 55275.j
• Number of curves: $1$
• Conductor: $55275$
• CM: no
• Rank: $1$

Rank

The elliptic curve 55275.j1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(67\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 55275.j do not have complex multiplication.

Modular form 55275.2.a.j

Elliptic curves in class 55275.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55275.j1	55275r1	\([0, 1, 1, -18833, -53307256]\)	\(-1891233955840/3140817904323\)	\(-1226881993876171875\)	\([]\)	\(946080\)	\(2.1499\)	\(\Gamma_0(N)\)-optimal