Elliptic curve isogeny class with LMFDB label 388080.nt (Cremona label 388080nt)

• Label: 388080.nt
• Number of curves: $4$
• Conductor: $388080$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 388080.nt have rank \(2\).

L-function data

Bad L-factors:

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

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.i
\(23\)	\( 1 + 23 T^{2}\)	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 388080.nt do not have complex multiplication.

Modular form 388080.2.a.nt

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 388080.nt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388080.nt1	388080nt4	\([0, 0, 0, -11307387, -14634836566]\)	\(455129268177961/4392300\)	\(1543006344266956800\)	\([2]\)	\(14155776\)	\(2.6514\)
388080.nt2	388080nt2	\([0, 0, 0, -723387, -217311766]\)	\(119168121961/10890000\)	\(3825635564298240000\)	\([2, 2]\)	\(7077888\)	\(2.3048\)
388080.nt3	388080nt1	\([0, 0, 0, -158907, 20560106]\)	\(1263214441/211200\)	\(74194144277299200\)	\([2]\)	\(3538944\)	\(1.9583\)	\(\Gamma_0(N)\)-optimal
388080.nt4	388080nt3	\([0, 0, 0, 828933, -1023586774]\)	\(179310732119/1392187500\)	\(-489072728390400000000\)	\([2]\)	\(14155776\)	\(2.6514\)