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

• Label: 333200.ga
• Number of curves: $4$
• Conductor: $333200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 333200.ga 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 \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 333200.2.a.ga

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 333200.ga

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
333200.ga1	333200ga3	\([0, -1, 0, -81703008, -55885535488]\)	\(8010684753304969/4456448000000\)	\(33554985648128000000000000\)	\([2]\)	\(99532800\)	\(3.5883\)
333200.ga2	333200ga1	\([0, -1, 0, -50049008, 136297560512]\)	\(1841373668746009/31443200\)	\(236752706355200000000\)	\([2]\)	\(33177600\)	\(3.0390\)	\(\Gamma_0(N)\)-optimal
333200.ga3	333200ga2	\([0, -1, 0, -48481008, 145235160512]\)	\(-1673672305534489/241375690000\)	\(-1817446947379840000000000\)	\([2]\)	\(66355200\)	\(3.3856\)
333200.ga4	333200ga4	\([0, -1, 0, 319704992, -442842847488]\)	\(479958568556831351/289000000000000\)	\(-2176035904000000000000000000\)	\([2]\)	\(199065600\)	\(3.9349\)