Elliptic curve isogeny class with LMFDB label 3328.j (Cremona label 3328b)

• Label: 3328.j
• Number of curves: $2$
• Conductor: $3328$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 3328.j have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3328.j do not have complex multiplication.

Modular form 3328.2.a.j

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 3328.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3328.j1	3328b2	\([0, 1, 0, -29, -5317]\)	\(-85184/371293\)	\(-12166529024\)	\([]\)	\(1920\)	\(0.61410\)
3328.j2	3328b1	\([0, 1, 0, -29, 59]\)	\(-85184/13\)	\(-425984\)	\([]\)	\(384\)	\(-0.19062\)	\(\Gamma_0(N)\)-optimal