Elliptic curve isogeny class with LMFDB label 47775.by (Cremona label 47775cx)

• Label: 47775.by
• Number of curves: $1$
• Conductor: $47775$
• CM: no
• Rank: $1$

Rank

The elliptic curve 47775.by1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 47775.by do not have complex multiplication.

Modular form 47775.2.a.by

Elliptic curves in class 47775.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47775.by1	47775cx1	\([0, 1, 1, -4083, -107131]\)	\(-8028160/507\)	\(-475510546875\)	\([]\)	\(63360\)	\(0.99433\)	\(\Gamma_0(N)\)-optimal