Elliptic curve isogeny class with Cremona label 152880dg (LMFDB label 152880.dt)

• Label: 152880dg
• Number of curves: $4$
• Conductor: $152880$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 152880dg have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 152880dg do not have complex multiplication.

Modular form 152880.2.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 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 152880dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
152880.dt3	152880dg1	\([0, -1, 0, -10600, 410992]\)	\(273359449/9360\)	\(4510493245440\)	\([2]\)	\(294912\)	\(1.2000\)	\(\Gamma_0(N)\)-optimal
152880.dt2	152880dg2	\([0, -1, 0, -26280, -1069200]\)	\(4165509529/1368900\)	\(659659637145600\)	\([2, 2]\)	\(589824\)	\(1.5466\)
152880.dt4	152880dg3	\([0, -1, 0, 75640, -7429008]\)	\(99317171591/106616250\)	\(-51377337123840000\)	\([2]\)	\(1179648\)	\(1.8931\)
152880.dt1	152880dg4	\([0, -1, 0, -379080, -89692560]\)	\(12501706118329/2570490\)	\(1238694207528960\)	\([2]\)	\(1179648\)	\(1.8931\)