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

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

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	\([0, 0, 0, -102827, 12690966]\)	\(132304644/5\)	\(4544018846720\)	\([2]\)	\(115200\)	\(1.5148\)

Rank

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

Complex multiplication

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

Modular form 38440.2.a.e

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.