Elliptic curve isogeny class with LMFDB label 55440.dd (Cremona label 55440dw)

• Label: 55440.dd
• Number of curves: $4$
• Conductor: $55440$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 55440.dd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(11\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 55440.dd do not have complex multiplication.

Modular form 55440.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 55440.dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55440.dd1	55440dw4	\([0, 0, 0, -2253387, 1004694266]\)	\(423783056881319689/99207416000000\)	\(296231756857344000000\)	\([2]\)	\(1990656\)	\(2.6400\)
55440.dd2	55440dw2	\([0, 0, 0, -2107227, 1177375754]\)	\(346553430870203929/8300600\)	\(24785458790400\)	\([2]\)	\(663552\)	\(2.0907\)
55440.dd3	55440dw1	\([0, 0, 0, -131547, 18441866]\)	\(-84309998289049/414124480\)	\(-1236569071288320\)	\([2]\)	\(331776\)	\(1.7441\)	\(\Gamma_0(N)\)-optimal
55440.dd4	55440dw3	\([0, 0, 0, 327093, 97913594]\)	\(1296134247276791/2137096192000\)	\(-6381335035772928000\)	\([2]\)	\(995328\)	\(2.2934\)