Elliptic curve isogeny class with Cremona label 333200dg (LMFDB label 333200.dg)

• Label: 333200dg
• Number of curves: $2$
• Conductor: $333200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 333200dg have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 333200dg do not have complex multiplication.

Modular form 333200.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 333200dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
333200.dg2	333200dg1	\([0, 0, 0, -2845675, -8273931750]\)	\(-338463151209/3731840000\)	\(-28099023626240000000000\)	\([2]\)	\(13271040\)	\(2.9895\)	\(\Gamma_0(N)\)-optimal
333200.dg1	333200dg2	\([0, 0, 0, -81245675, -281027531750]\)	\(7876916680687209/27200448800\)	\(204806758455756800000000\)	\([2]\)	\(26542080\)	\(3.3361\)