Elliptic curve isogeny class with LMFDB label 33600.dn (Cremona label 33600by)

• Label: 33600.dn
• Number of curves: $1$
• Conductor: $33600$
• CM: no
• Rank: $1$

Rank

The elliptic curve 33600.dn1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 33600.dn do not have complex multiplication.

Modular form 33600.2.a.dn

Elliptic curves in class 33600.dn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33600.dn1	33600by1	\([0, -1, 0, 63167, 8026537]\)	\(69683121920/110270727\)	\(-44108290800000000\)	\([]\)	\(307200\)	\(1.8790\)	\(\Gamma_0(N)\)-optimal