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

• Label: 388080.gq
• Number of curves: $4$
• Conductor: $388080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 388080.gq have rank \(1\).

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
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 388080.gq do not have complex multiplication.

Modular form 388080.2.a.gq

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 388080.gq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388080.gq1	388080gq3	\([0, 0, 0, -74511367203, 7828560497127202]\)	\(130231365028993807856757649/4753980000\)	\(1670063816341831680000\)	\([2]\)	\(566231040\)	\(4.4906\)
388080.gq2	388080gq4	\([0, 0, 0, -4743897123, 117516946662178]\)	\(33608860073906150870929/2466782226562500000\)	\(866575740616740000000000000000\)	\([2]\)	\(566231040\)	\(4.4906\)
388080.gq3	388080gq2	\([0, 0, 0, -4656967203, 122320885287202]\)	\(31794905164720991157649/192099600000000\)	\(67484211354220953600000000\)	\([2, 2]\)	\(283115520\)	\(4.1440\)
388080.gq4	388080gq1	\([0, 0, 0, -285634083, 1985952893218]\)	\(-7336316844655213969/604492922880000\)	\(-212357173933546489774080000\)	\([2]\)	\(141557760\)	\(3.7975\)	\(\Gamma_0(N)\)-optimal