Elliptic curve isogeny class with Cremona label 159600bn (LMFDB label 159600.gv)

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

Rank

The elliptic curves in class 159600bn 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 159600.2.a.bn

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 159600bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
159600.gv3	159600bn1	\([0, 1, 0, -64608, 3676788]\)	\(466025146777/177366672\)	\(11351467008000000\)	\([2]\)	\(983040\)	\(1.7800\)	\(\Gamma_0(N)\)-optimal
159600.gv2	159600bn2	\([0, 1, 0, -456608, -116275212]\)	\(164503536215257/4178071044\)	\(267396546816000000\)	\([2, 2]\)	\(1966080\)	\(2.1266\)
159600.gv4	159600bn3	\([0, 1, 0, 75392, -370571212]\)	\(740480746823/927484650666\)	\(-59359017642624000000\)	\([2]\)	\(3932160\)	\(2.4732\)
159600.gv1	159600bn4	\([0, 1, 0, -7260608, -7532635212]\)	\(661397832743623417/443352042\)	\(28374530688000000\)	\([2]\)	\(3932160\)	\(2.4732\)