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

• Label: 302016.dc
• Number of curves: $4$
• Conductor: $302016$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 302016.dc have rank \(0\).

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.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 302016.2.a.dc

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 302016.dc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
302016.dc1	302016dc3	\([0, -1, 0, -318929057, 2192352113217]\)	\(7725203825376001537/7722\)	\(3586128358146048\)	\([4]\)	\(26542080\)	\(3.1729\)
302016.dc2	302016dc4	\([0, -1, 0, -20785057, 31173041473]\)	\(2138362647385537/333926700822\)	\(155076924548034892136448\)	\([2]\)	\(26542080\)	\(3.1729\)
302016.dc3	302016dc2	\([0, -1, 0, -19933217, 34259939265]\)	\(1886079023633377/59629284\)	\(27692083181603782656\)	\([2, 2]\)	\(13271040\)	\(2.8264\)
302016.dc4	302016dc1	\([0, -1, 0, -1192737, 583296705]\)	\(-404075127457/82223856\)	\(-38185094757539119104\)	\([2]\)	\(6635520\)	\(2.4798\)	\(\Gamma_0(N)\)-optimal