Elliptic curve isogeny class with Cremona label 40362w (LMFDB label 40362.w)

• Label: 40362w
• Number of curves: $4$
• Conductor: $40362$
• CM: no
• Rank: $1$

Elliptic curves in class 40362w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40362.w3	40362w1	\([1, 1, 1, -1921059, 1024022337]\)	\(883437180088177/24498432\)	\(21742448578728192\)	\([4]\)	\(737280\)	\(2.2377\)	\(\Gamma_0(N)\)-optimal
40362.w2	40362w2	\([1, 1, 1, -1997939, 937516961]\)	\(993802845830257/146526652944\)	\(130042943852409486864\)	\([2, 2]\)	\(1474560\)	\(2.5843\)
40362.w4	40362w3	\([1, 1, 1, 3364441, 5109448601]\)	\(4745612697439823/15446876516316\)	\(-13709159768182906559196\)	\([2]\)	\(2949120\)	\(2.9308\)
40362.w1	40362w4	\([1, 1, 1, -8590399, -8769221143]\)	\(78993900837812017/8313251597532\)	\(7378041393888780515292\)	\([2]\)	\(2949120\)	\(2.9308\)

Rank

The elliptic curves in class 40362w have rank \(1\).

Complex multiplication

The elliptic curves in class 40362w do not have complex multiplication.

Modular form 40362.2.a.w

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.