Elliptic curve isogeny class with LMFDB label 38640.cg (Cremona label 38640ct)

• Label: 38640.cg
• Number of curves: $4$
• Conductor: $38640$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 38640.cg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1 - T\)
\(23\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 38640.cg do not have complex multiplication.

Modular form 38640.2.a.cg

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 38640.cg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38640.cg1	38640ct4	\([0, 1, 0, -80816, -8869740]\)	\(14251520160844849/264449745\)	\(1083186155520\)	\([2]\)	\(122880\)	\(1.4342\)
38640.cg2	38640ct2	\([0, 1, 0, -5216, -130380]\)	\(3832302404449/472410225\)	\(1934992281600\)	\([2, 2]\)	\(61440\)	\(1.0876\)
38640.cg3	38640ct1	\([0, 1, 0, -1296, 15444]\)	\(58818484369/7455105\)	\(30536110080\)	\([2]\)	\(30720\)	\(0.74103\)	\(\Gamma_0(N)\)-optimal
38640.cg4	38640ct3	\([0, 1, 0, 7664, -661036]\)	\(12152722588271/53476250625\)	\(-219038722560000\)	\([2]\)	\(122880\)	\(1.4342\)