Elliptic curve isogeny class with Cremona label 62400bf (LMFDB label 62400.dy)

• Label: 62400bf
• Number of curves: $4$
• Conductor: $62400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 62400bf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 62400bf do not have complex multiplication.

Modular form 62400.2.a.bf

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 62400bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
62400.dy4	62400bf1	\([0, -1, 0, 767, -17663]\)	\(12167/39\)	\(-159744000000\)	\([2]\)	\(65536\)	\(0.83293\)	\(\Gamma_0(N)\)-optimal
62400.dy3	62400bf2	\([0, -1, 0, -7233, -201663]\)	\(10218313/1521\)	\(6230016000000\)	\([2, 2]\)	\(131072\)	\(1.1795\)
62400.dy2	62400bf3	\([0, -1, 0, -31233, 1934337]\)	\(822656953/85683\)	\(350957568000000\)	\([2]\)	\(262144\)	\(1.5261\)
62400.dy1	62400bf4	\([0, -1, 0, -111233, -14241663]\)	\(37159393753/1053\)	\(4313088000000\)	\([2]\)	\(262144\)	\(1.5261\)