Elliptic curve isogeny class with LMFDB label 51600.dq (Cremona label 51600di)

• Label: 51600.dq
• Number of curves: $4$
• Conductor: $51600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 51600.dq have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 51600.dq do not have complex multiplication.

Modular form 51600.2.a.dq

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 51600.dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51600.dq1	51600di4	\([0, 1, 0, -2073008, 990587988]\)	\(15393836938735081/2275690697640\)	\(145644204648960000000\)	\([2]\)	\(1658880\)	\(2.5936\)
51600.dq2	51600di3	\([0, 1, 0, -1993008, 1082267988]\)	\(13679527032530281/381633600\)	\(24424550400000000\)	\([2]\)	\(829440\)	\(2.2471\)
51600.dq3	51600di2	\([0, 1, 0, -543008, -154032012]\)	\(276670733768281/336980250\)	\(21566736000000000\)	\([2]\)	\(552960\)	\(2.0443\)
51600.dq4	51600di1	\([0, 1, 0, -43008, -1032012]\)	\(137467988281/72562500\)	\(4644000000000000\)	\([2]\)	\(276480\)	\(1.6978\)	\(\Gamma_0(N)\)-optimal