Elliptic curve isogeny class with Cremona label 92400dw (LMFDB label 92400.z)

• Label: 92400dw
• Number of curves: $4$
• Conductor: $92400$
• CM: no
• Rank: $1$

Elliptic curves in class 92400dw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
92400.z3	92400dw1	\([0, -1, 0, -200408, 30051312]\)	\(13908844989649/1980372240\)	\(126743823360000000\)	\([2]\)	\(884736\)	\(2.0075\)	\(\Gamma_0(N)\)-optimal
92400.z2	92400dw2	\([0, -1, 0, -848408, -270620688]\)	\(1055257664218129/115307784900\)	\(7379698233600000000\)	\([2, 2]\)	\(1769472\)	\(2.3541\)
92400.z4	92400dw3	\([0, -1, 0, 1131592, -1347740688]\)	\(2503876820718671/13702874328990\)	\(-876983957055360000000\)	\([2]\)	\(3538944\)	\(2.7006\)
92400.z1	92400dw4	\([0, -1, 0, -13196408, -18446876688]\)	\(3971101377248209009/56495958750\)	\(3615741360000000000\)	\([2]\)	\(3538944\)	\(2.7006\)

Rank

The elliptic curves in class 92400dw have rank \(1\).

Complex multiplication

The elliptic curves in class 92400dw do not have complex multiplication.

Modular form 92400.2.a.dw

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.