Elliptic curve isogeny class with Cremona label 302016dg (LMFDB label 302016.dg)

• Label: 302016dg
• Number of curves: $4$
• Conductor: $302016$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 302016dg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 302016dg do not have complex multiplication.

Modular form 302016.2.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 302016dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
302016.dg4	302016dg1	\([0, -1, 0, -11172, 68598]\)	\(1360251712/771147\)	\(87432572829888\)	\([2]\)	\(983040\)	\(1.3651\)	\(\Gamma_0(N)\)-optimal
302016.dg2	302016dg2	\([0, -1, 0, -113417, -14593335]\)	\(22235451328/123201\)	\(893985123373056\)	\([2, 2]\)	\(1966080\)	\(1.7117\)
302016.dg3	302016dg3	\([0, -1, 0, -50497, -30763775]\)	\(-245314376/6908733\)	\(-401055479962435584\)	\([2]\)	\(3932160\)	\(2.0582\)
302016.dg1	302016dg4	\([0, -1, 0, -1812257, -938422527]\)	\(11339065490696/351\)	\(20375729307648\)	\([2]\)	\(3932160\)	\(2.0582\)