Elliptic curve isogeny class with Cremona label 159600gy (LMFDB label 159600.bo)

• Label: 159600gy
• Number of curves: $4$
• Conductor: $159600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 159600gy have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 159600gy do not have complex multiplication.

Modular form 159600.2.a.gy

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 159600gy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
159600.bo4	159600gy1	\([0, -1, 0, -108983, 5460462]\)	\(572616640141312/280535480757\)	\(70133870189250000\)	\([2]\)	\(1572864\)	\(1.9257\)	\(\Gamma_0(N)\)-optimal
159600.bo2	159600gy2	\([0, -1, 0, -929108, -340632288]\)	\(22174957026242512/278654127129\)	\(1114616508516000000\)	\([2, 2]\)	\(3145728\)	\(2.2723\)
159600.bo3	159600gy3	\([0, -1, 0, -159608, -888516288]\)	\(-28104147578308/21301741002339\)	\(-340827856037424000000\)	\([2]\)	\(6291456\)	\(2.6189\)
159600.bo1	159600gy4	\([0, -1, 0, -14820608, -21955806288]\)	\(22501000029889239268/3620708343\)	\(57931333488000000\)	\([2]\)	\(6291456\)	\(2.6189\)