Elliptic curve isogeny class with Cremona label 290160dq (LMFDB label 290160.dq)

• Label: 290160dq
• Number of curves: $4$
• Conductor: $290160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 290160dq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)
\(31\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 290160dq do not have complex multiplication.

Modular form 290160.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 290160dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
290160.dq4	290160dq1	\([0, 0, 0, -5518587, 4989876266]\)	\(6224721371657832889/2942222400\)	\(8785429010841600\)	\([2]\)	\(7299072\)	\(2.3964\)	\(\Gamma_0(N)\)-optimal
290160.dq3	290160dq2	\([0, 0, 0, -5547387, 4935162026]\)	\(6322686217296773689/135260510172840\)	\(403885719207937474560\)	\([2]\)	\(14598144\)	\(2.7430\)
290160.dq2	290160dq3	\([0, 0, 0, -6557547, 2980207514]\)	\(10443846301537515049/4758933504000000\)	\(14210099300007936000000\)	\([2]\)	\(21897216\)	\(2.9457\)
290160.dq1	290160dq4	\([0, 0, 0, -52637547, -144945808486]\)	\(5401609226997647595049/86393158323264000\)	\(257968588462733131776000\)	\([2]\)	\(43794432\)	\(3.2923\)