Elliptic curve isogeny class with LMFDB label 163800.dg (Cremona label 163800w)

• Label: 163800.dg
• Number of curves: $4$
• Conductor: $163800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 163800.dg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 163800.dg do not have complex multiplication.

Modular form 163800.2.a.dg

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 163800.dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
163800.dg1	163800w3	\([0, 0, 0, -5619675, 5127601750]\)	\(841356017734178/1404585\)	\(32766158880000000\)	\([2]\)	\(3932160\)	\(2.4312\)
163800.dg2	163800w4	\([0, 0, 0, -921675, -235084250]\)	\(3711757787138/1124589375\)	\(26234420940000000000\)	\([2]\)	\(3932160\)	\(2.4312\)
163800.dg3	163800w2	\([0, 0, 0, -354675, 78466750]\)	\(423026849956/16769025\)	\(195593907600000000\)	\([2, 2]\)	\(1966080\)	\(2.0846\)
163800.dg4	163800w1	\([0, 0, 0, 9825, 4473250]\)	\(35969456/2985255\)	\(-8705003580000000\)	\([2]\)	\(983040\)	\(1.7381\)	\(\Gamma_0(N)\)-optimal