Elliptic curve isogeny class with Cremona label 100800ft (LMFDB label 100800.iv)

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

Elliptic curves in class 100800ft

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.iv3	100800ft1	\([0, 0, 0, -50700, 2774000]\)	\(4826809/1680\)	\(5016453120000000\)	\([2]\)	\(589824\)	\(1.7142\)	\(\Gamma_0(N)\)-optimal
100800.iv2	100800ft2	\([0, 0, 0, -338700, -73834000]\)	\(1439069689/44100\)	\(131681894400000000\)	\([2, 2]\)	\(1179648\)	\(2.0608\)
100800.iv4	100800ft3	\([0, 0, 0, 93300, -249226000]\)	\(30080231/9003750\)	\(-26885053440000000000\)	\([2]\)	\(2359296\)	\(2.4073\)
100800.iv1	100800ft4	\([0, 0, 0, -5378700, -4801354000]\)	\(5763259856089/5670\)	\(16930529280000000\)	\([2]\)	\(2359296\)	\(2.4073\)

Rank

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

Complex multiplication

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

Modular form 100800.2.a.ft

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.