Elliptic curve isogeny class with LMFDB label 321600.jn (Cremona label 321600jn)

• Label: 321600.jn
• Number of curves: $4$
• Conductor: $321600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 321600.jn have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(67\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	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 321600.jn do not have complex multiplication.

Modular form 321600.2.a.jn

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 321600.jn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
321600.jn1	321600jn3	\([0, 1, 0, -469633, 90288863]\)	\(5593330773938/1511334075\)	\(3095212185600000000\)	\([2]\)	\(6291456\)	\(2.2561\)
321600.jn2	321600jn2	\([0, 1, 0, -169633, -25811137]\)	\(527178079876/25250625\)	\(25856640000000000\)	\([2, 2]\)	\(3145728\)	\(1.9095\)
321600.jn3	321600jn1	\([0, 1, 0, -167633, -26473137]\)	\(2035002230224/5025\)	\(1286400000000\)	\([2]\)	\(1572864\)	\(1.5629\)	\(\Gamma_0(N)\)-optimal
321600.jn4	321600jn4	\([0, 1, 0, 98367, -99511137]\)	\(51396982702/2119921875\)	\(-4341600000000000000\)	\([2]\)	\(6291456\)	\(2.2561\)