Elliptic curve isogeny class with LMFDB label 464.d (Cremona label 464a)

• Label: 464.d
• Number of curves: $1$
• Conductor: $464$
• CM: no
• Rank: $1$

Rank

The elliptic curve 464.d1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 464.d do not have complex multiplication.

Modular form 464.2.a.d

Isogeny graph

Elliptic curves in class 464.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
464.d1	464a1	\([0, 1, 0, 8, 4]\)	\(48668/29\)	\(-29696\)	\([]\)	\(32\)	\(-0.45245\)	\(\Gamma_0(N)\)-optimal