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

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

Rank

The elliptic curves in class 382200cs 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 382200.2.a.cs

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 382200cs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
382200.cs4	382200cs1	\([0, -1, 0, 206617, -2480988]\)	\(33165879296/19278675\)	\(-567029208768750000\)	\([2]\)	\(3538944\)	\(2.0960\)	\(\Gamma_0(N)\)-optimal
382200.cs3	382200cs2	\([0, -1, 0, -828508, -19042988]\)	\(133649126224/77000625\)	\(36236186122500000000\)	\([2, 2]\)	\(7077888\)	\(2.4426\)
382200.cs2	382200cs3	\([0, -1, 0, -8791008, 9997782012]\)	\(39914580075556/172718325\)	\(325122211486800000000\)	\([2]\)	\(14155776\)	\(2.7892\)
382200.cs1	382200cs4	\([0, -1, 0, -9428008, -11112397988]\)	\(49235161015876/137109375\)	\(258092493750000000000\)	\([2]\)	\(14155776\)	\(2.7892\)