Elliptic curve isogeny class with LMFDB label 48510.dp (Cremona label 48510dt)

• Label: 48510.dp
• Number of curves: $4$
• Conductor: $48510$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 48510.dp have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 48510.dp do not have complex multiplication.

Modular form 48510.2.a.dp

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 48510.dp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48510.dp1	48510dt4	\([1, -1, 1, -706712, 228845999]\)	\(455129268177961/4392300\)	\(376710533268300\)	\([2]\)	\(589824\)	\(1.9583\)
48510.dp2	48510dt2	\([1, -1, 1, -45212, 3406799]\)	\(119168121961/10890000\)	\(933993057690000\)	\([2, 2]\)	\(294912\)	\(1.6117\)
48510.dp3	48510dt1	\([1, -1, 1, -9932, -318769]\)	\(1263214441/211200\)	\(18113804755200\)	\([2]\)	\(147456\)	\(1.2651\)	\(\Gamma_0(N)\)-optimal
48510.dp4	48510dt3	\([1, -1, 1, 51808, 15980591]\)	\(179310732119/1392187500\)	\(-119402521579687500\)	\([2]\)	\(589824\)	\(1.9583\)