Elliptic curve isogeny class with Cremona label 385434dq (LMFDB label 385434.dq)

• Label: 385434dq
• Number of curves: $4$
• Conductor: $385434$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 385434dq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1 + T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 385434dq do not have complex multiplication.

Modular form 385434.2.a.dq

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 385434dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
385434.dq3	385434dq1	\([1, -1, 1, -86666, 9818057]\)	\(839362385737/2349312\)	\(201491377258752\)	\([2]\)	\(1769472\)	\(1.6170\)	\(\Gamma_0(N)\)-optimal
385434.dq2	385434dq2	\([1, -1, 1, -121946, 1096841]\)	\(2338337977417/1347477264\)	\(115567898068972944\)	\([2, 2]\)	\(3538944\)	\(1.9636\)
385434.dq4	385434dq3	\([1, -1, 1, 486634, 8399801]\)	\(148599082115063/86360598996\)	\(-7406813583123414516\)	\([2]\)	\(7077888\)	\(2.3102\)
385434.dq1	385434dq4	\([1, -1, 1, -1295006, -564787303]\)	\(2800418713303177/12058908372\)	\(1034245794560865012\)	\([2]\)	\(7077888\)	\(2.3102\)