Elliptic curve isogeny class with Cremona label 4640a (LMFDB label 4640.d)

• Label: 4640a
• Number of curves: $2$
• Conductor: $4640$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 4640a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4640a do not have complex multiplication.

Modular form 4640.2.a.a

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 4640a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4640.d1	4640a1	\([0, 0, 0, -193, 1032]\)	\(12422690496/145\)	\(9280\)	\([2]\)	\(384\)	\(-0.087988\)	\(\Gamma_0(N)\)-optimal
4640.d2	4640a2	\([0, 0, 0, -188, 1088]\)	\(-179406144/21025\)	\(-86118400\)	\([2]\)	\(768\)	\(0.25858\)