Elliptic curve isogeny class with LMFDB label 45760.by (Cremona label 45760b)

• Label: 45760.by
• Number of curves: $1$
• Conductor: $45760$
• CM: no
• Rank: $1$

Rank

The elliptic curve 45760.by1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 45760.by do not have complex multiplication.

Modular form 45760.2.a.by

Elliptic curves in class 45760.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
45760.by1	45760b1	\([0, 0, 0, -195628, 67848752]\)	\(-3158470573163361/5758438400000\)	\(-1509540075929600000\)	\([]\)	\(1198080\)	\(2.1783\)	\(\Gamma_0(N)\)-optimal