Elliptic curve isogeny class with LMFDB label 216384.dq (Cremona label 216384iq)

• Label: 216384.dq
• Number of curves: $4$
• Conductor: $216384$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 216384.dq have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.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 216384.dq do not have complex multiplication.

Modular form 216384.2.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 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 216384.dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
216384.dq1	216384iq4	\([0, -1, 0, -147457, -18393983]\)	\(45989074372/7555707\)	\(58256351090638848\)	\([2]\)	\(1769472\)	\(1.9386\)
216384.dq2	216384iq2	\([0, -1, 0, -41617, 3006865]\)	\(4135597648/385641\)	\(743346634899456\)	\([2, 2]\)	\(884736\)	\(1.5920\)
216384.dq3	216384iq1	\([0, -1, 0, -40637, 3166605]\)	\(61604313088/621\)	\(74813469696\)	\([2]\)	\(442368\)	\(1.2455\)	\(\Gamma_0(N)\)-optimal
216384.dq4	216384iq3	\([0, -1, 0, 48543, 14168673]\)	\(1640689628/12223143\)	\(-94243425537687552\)	\([2]\)	\(1769472\)	\(1.9386\)