Elliptic curve isogeny class with LMFDB label 100800.eh (Cremona label 100800kx)

• Label: 100800.eh
• Number of curves: $4$
• Conductor: $100800$
• CM: no
• Rank: $1$

Elliptic curves in class 100800.eh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.eh1	100800kx4	\([0, 0, 0, -2016300, -1101998000]\)	\(1214399773444/105\)	\(78382080000000\)	\([2]\)	\(786432\)	\(2.1066\)
100800.eh2	100800kx2	\([0, 0, 0, -126300, -17138000]\)	\(1193895376/11025\)	\(2057529600000000\)	\([2, 2]\)	\(393216\)	\(1.7600\)
100800.eh3	100800kx3	\([0, 0, 0, -36300, -41078000]\)	\(-7086244/972405\)	\(-725896442880000000\)	\([2]\)	\(786432\)	\(2.1066\)
100800.eh4	100800kx1	\([0, 0, 0, -13800, 187000]\)	\(24918016/13125\)	\(153090000000000\)	\([2]\)	\(196608\)	\(1.4135\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 100800.eh have rank \(1\).

Complex multiplication

The elliptic curves in class 100800.eh do not have complex multiplication.

Modular form 100800.2.a.eh

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.