Elliptic curve isogeny class with Cremona label 320320dl (LMFDB label 320320.dl)

• Label: 320320dl
• Number of curves: $4$
• Conductor: $320320$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 320320dl have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 320320dl do not have complex multiplication.

Modular form 320320.2.a.dl

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 Cremona 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 Cremona labels.

Elliptic curves in class 320320dl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
320320.dl3	320320dl1	\([0, 0, 0, -33452, -2354896]\)	\(15792469779969/400400\)	\(104962457600\)	\([2]\)	\(688128\)	\(1.2225\)	\(\Gamma_0(N)\)-optimal
320320.dl2	320320dl2	\([0, 0, 0, -34732, -2164944]\)	\(17675559395649/2505002500\)	\(656671375360000\)	\([2, 2]\)	\(1376256\)	\(1.5691\)
320320.dl1	320320dl3	\([0, 0, 0, -146732, 19473456]\)	\(1332779492447649/146356560350\)	\(38366494156390400\)	\([4]\)	\(2752512\)	\(1.9157\)
320320.dl4	320320dl4	\([0, 0, 0, 56788, -11646416]\)	\(77259787831071/268236718750\)	\(-70316646400000000\)	\([2]\)	\(2752512\)	\(1.9157\)