Elliptic curve isogeny class with LMFDB label 3192.n (Cremona label 3192f)

• Label: 3192.n
• Number of curves: $2$
• Conductor: $3192$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 3192.n have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3192.n do not have complex multiplication.

Modular form 3192.2.a.n

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 3192.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3192.n1	3192f2	\([0, 1, 0, -168, -864]\)	\(515150500/22743\)	\(23288832\)	\([2]\)	\(768\)	\(0.17662\)
3192.n2	3192f1	\([0, 1, 0, -28, 32]\)	\(9826000/2793\)	\(715008\)	\([2]\)	\(384\)	\(-0.16995\)	\(\Gamma_0(N)\)-optimal