Elliptic curve isogeny class with LMFDB label 3328.g (Cremona label 3328k)

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

Rank

The elliptic curves in class 3328.g 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.d
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 11 T^{2}\)	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.ae
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 3328.2.a.g

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.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3328.g1	3328k1	\([0, 1, 0, -7, -11]\)	\(-85184/13\)	\(-6656\)	\([]\)	\(192\)	\(-0.53720\)	\(\Gamma_0(N)\)-optimal
3328.g2	3328k2	\([0, 1, 0, -7, 661]\)	\(-85184/371293\)	\(-190102016\)	\([]\)	\(960\)	\(0.26752\)