Elliptic curve isogeny class with Cremona label 38440e (LMFDB label 38440.g)

• Label: 38440e
• Number of curves: $4$
• Conductor: $38440$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 38440e have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 38440e do not have complex multiplication.

Modular form 38440.2.a.e

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 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 38440e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38440.g3	38440e1	\([0, 0, 0, -1922, -29791]\)	\(55296/5\)	\(71000294480\)	\([2]\)	\(28800\)	\(0.82163\)	\(\Gamma_0(N)\)-optimal
38440.g2	38440e2	\([0, 0, 0, -6727, 178746]\)	\(148176/25\)	\(5680023558400\)	\([2, 2]\)	\(57600\)	\(1.1682\)
38440.g4	38440e3	\([0, 0, 0, 12493, 1012894]\)	\(237276/625\)	\(-568002355840000\)	\([2]\)	\(115200\)	\(1.5148\)
38440.g1	38440e4	\([0, 0, 0, -102827, 12690966]\)	\(132304644/5\)	\(4544018846720\)	\([2]\)	\(115200\)	\(1.5148\)