Elliptic curve isogeny class with Cremona label 299880dn (LMFDB label 299880.dn)

• Label: 299880dn
• Number of curves: $2$
• Conductor: $299880$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 299880dn have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 299880dn do not have complex multiplication.

Modular form 299880.2.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 299880dn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
299880.dn2	299880dn1	\([0, 0, 0, -279488307, -2752333576706]\)	\(-27491530342319084164/21352892495484375\)	\(-1875307275742929776496000000\)	\([2]\)	\(123863040\)	\(3.9319\)	\(\Gamma_0(N)\)-optimal
299880.dn1	299880dn2	\([0, 0, 0, -5101823307, -140228424223706]\)	\(83609231549925663172082/22317062975463375\)	\(3919970147365297871500032000\)	\([2]\)	\(247726080\)	\(4.2785\)