Elliptic curve isogeny class with LMFDB label 320.c (Cremona label 320b)

• Label: 320.c
• Number of curves: $4$
• Conductor: $320$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 320.c have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 320.c do not have complex multiplication.

Modular form 320.2.a.c

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 320.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
320.c1	320b3	\([0, 0, 0, -428, -3408]\)	\(132304644/5\)	\(327680\)	\([2]\)	\(64\)	\(0.14436\)
320.c2	320b2	\([0, 0, 0, -28, -48]\)	\(148176/25\)	\(409600\)	\([2, 2]\)	\(32\)	\(-0.20221\)
320.c3	320b1	\([0, 0, 0, -8, 8]\)	\(55296/5\)	\(5120\)	\([2]\)	\(16\)	\(-0.54879\)	\(\Gamma_0(N)\)-optimal
320.c4	320b4	\([0, 0, 0, 52, -272]\)	\(237276/625\)	\(-40960000\)	\([2]\)	\(64\)	\(0.14436\)