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

• Label: 3192.f
• Number of curves: $2$
• Conductor: $3192$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 3192.f have rank \(1\).

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
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 3192.2.a.f

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.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3192.f1	3192e2	\([0, -1, 0, -708, -7020]\)	\(153531250000/1197\)	\(306432\)	\([2]\)	\(768\)	\(0.22614\)
3192.f2	3192e1	\([0, -1, 0, -43, -104]\)	\(-562432000/53067\)	\(-849072\)	\([2]\)	\(384\)	\(-0.12043\)	\(\Gamma_0(N)\)-optimal