Elliptic curve isogeny class with Cremona label 382200jg (LMFDB label 382200.jg)

• Label: 382200jg
• Number of curves: $4$
• Conductor: $382200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 382200jg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 382200jg do not have complex multiplication.

Modular form 382200.2.a.jg

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 382200jg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
382200.jg3	382200jg1	\([0, 1, 0, -136383, -19385262]\)	\(9538484224/26325\)	\(774277481250000\)	\([2]\)	\(2654208\)	\(1.7298\)	\(\Gamma_0(N)\)-optimal
382200.jg2	382200jg2	\([0, 1, 0, -191508, -2296512]\)	\(1650587344/950625\)	\(447360322500000000\)	\([2, 2]\)	\(5308416\)	\(2.0764\)
382200.jg1	382200jg3	\([0, 1, 0, -2029008, 1107553488]\)	\(490757540836/2142075\)	\(4032207706800000000\)	\([2]\)	\(10616832\)	\(2.4230\)
382200.jg4	382200jg4	\([0, 1, 0, 763992, -17584512]\)	\(26198797244/15234375\)	\(-28676943750000000000\)	\([2]\)	\(10616832\)	\(2.4230\)