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

• Label: 302016dn
• Number of curves: $2$
• Conductor: $302016$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 302016dn 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
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 302016.2.a.dn

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 302016dn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
302016.dn2	302016dn1	\([0, -1, 0, -423177, 111440265]\)	\(-1154981015488/69090879\)	\(-501345102610919424\)	\([2]\)	\(6082560\)	\(2.1517\)	\(\Gamma_0(N)\)-optimal
302016.dn1	302016dn2	\([0, -1, 0, -6865217, 6925830177]\)	\(616425416371016/2024451\)	\(117520414736744448\)	\([2]\)	\(12165120\)	\(2.4983\)