Elliptic curve isogeny class with Cremona label 52416dd (LMFDB label 52416.fg)

• Label: 52416dd
• Number of curves: $4$
• Conductor: $52416$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 52416dd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 52416dd do not have complex multiplication.

Modular form 52416.2.a.dd

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 52416dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52416.fg3	52416dd1	\([0, 0, 0, -4044, 88688]\)	\(38272753/4368\)	\(834737799168\)	\([2]\)	\(73728\)	\(1.0199\)	\(\Gamma_0(N)\)-optimal
52416.fg2	52416dd2	\([0, 0, 0, -15564, -653200]\)	\(2181825073/298116\)	\(56970854793216\)	\([2, 2]\)	\(147456\)	\(1.3664\)
52416.fg4	52416dd3	\([0, 0, 0, 24756, -3475600]\)	\(8780064047/32388174\)	\(-6189476438605824\)	\([2]\)	\(294912\)	\(1.7130\)
52416.fg1	52416dd4	\([0, 0, 0, -240204, -45311632]\)	\(8020417344913/187278\)	\(35789383139328\)	\([2]\)	\(294912\)	\(1.7130\)