Elliptic curve isogeny class with LMFDB label 266175.bz (Cremona label 266175bz)

• Label: 266175.bz
• Number of curves: $1$
• Conductor: $266175$
• CM: no
• Rank: $2$

Rank

The elliptic curve 266175.bz1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 266175.bz do not have complex multiplication.

Modular form 266175.2.a.bz

Elliptic curves in class 266175.bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
266175.bz1	266175bz1	\([0, 0, 1, -50700, -4492719]\)	\(-7487094784/196875\)	\(-378987451171875\)	\([]\)	\(921600\)	\(1.5800\)	\(\Gamma_0(N)\)-optimal