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

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

Rank

The elliptic curve 45760b1 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.d
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 45760.2.a.b

Elliptic curves in class 45760b

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