Elliptic curve isogeny class with LMFDB label 166600.v (Cremona label 166600bd)

• Label: 166600.v
• Number of curves: $4$
• Conductor: $166600$
• CM: no
• Rank: $1$

Elliptic curves in class 166600.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
166600.v1	166600bd3	\([0, 0, 0, -1424675, 640466750]\)	\(84944038338/2088025\)	\(7860929703200000000\)	\([2]\)	\(2359296\)	\(2.4095\)
166600.v2	166600bd2	\([0, 0, 0, -199675, -19808250]\)	\(467720676/180625\)	\(340005610000000000\)	\([2, 2]\)	\(1179648\)	\(2.0630\)
166600.v3	166600bd1	\([0, 0, 0, -175175, -28211750]\)	\(1263257424/425\)	\(200003300000000\)	\([2]\)	\(589824\)	\(1.7164\)	\(\Gamma_0(N)\)-optimal
166600.v4	166600bd4	\([0, 0, 0, 633325, -142259250]\)	\(7462174302/6640625\)	\(-25000412500000000000\)	\([2]\)	\(2359296\)	\(2.4095\)

Rank

The elliptic curves in class 166600.v have rank \(1\).

Complex multiplication

The elliptic curves in class 166600.v do not have complex multiplication.

Modular form 166600.2.a.v

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.