Elliptic curve isogeny class with LMFDB label 40320.do (Cremona label 40320ds)

• Label: 40320.do
• Number of curves: $2$
• Conductor: $40320$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 40320.do have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 40320.do do not have complex multiplication.

Modular form 40320.2.a.do

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 40320.do

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40320.do1	40320ds1	\([0, 0, 0, -1497, 22286]\)	\(3976047968/1575\)	\(146966400\)	\([2]\)	\(16384\)	\(0.53132\)	\(\Gamma_0(N)\)-optimal
40320.do2	40320ds2	\([0, 0, 0, -1272, 29216]\)	\(-19056256/19845\)	\(-237027409920\)	\([2]\)	\(32768\)	\(0.87789\)