Elliptic curve isogeny class with Cremona label 24640w (LMFDB label 24640.bu)

• Label: 24640w
• Number of curves: $4$
• Conductor: $24640$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 24640w have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 + T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 24640w do not have complex multiplication.

Modular form 24640.2.a.w

Isogeny matrix

The \(i,j\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 24640w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
24640.bu3	24640w1	\([0, -1, 0, -58465, 5483745]\)	\(-84309998289049/414124480\)	\(-108560247685120\)	\([2]\)	\(110592\)	\(1.5414\)	\(\Gamma_0(N)\)-optimal
24640.bu2	24640w2	\([0, -1, 0, -936545, 349164257]\)	\(346553430870203929/8300600\)	\(2175952486400\)	\([2]\)	\(221184\)	\(1.8879\)
24640.bu4	24640w3	\([0, -1, 0, 145375, 28962977]\)	\(1296134247276791/2137096192000\)	\(-560226944155648000\)	\([2]\)	\(331776\)	\(2.0907\)
24640.bu1	24640w4	\([0, -1, 0, -1001505, 298021025]\)	\(423783056881319689/99207416000000\)	\(26006628859904000000\)	\([2]\)	\(663552\)	\(2.4372\)