Elliptic curve isogeny class with Cremona label 189630r (LMFDB label 189630.ey)

• Label: 189630r
• Number of curves: $4$
• Conductor: $189630$
• CM: no
• Rank: $0$

Elliptic curves in class 189630r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
189630.ey4	189630r1	\([1, -1, 1, -47417, 1189941]\)	\(137467988281/72562500\)	\(6223404155062500\)	\([2]\)	\(1382400\)	\(1.7222\)	\(\Gamma_0(N)\)-optimal
189630.ey3	189630r2	\([1, -1, 1, -598667, 178251441]\)	\(276670733768281/336980250\)	\(28901488896110250\)	\([2]\)	\(2764800\)	\(2.0687\)
189630.ey2	189630r3	\([1, -1, 1, -2197292, -1253080209]\)	\(13679527032530281/381633600\)	\(32731233515265600\)	\([2]\)	\(4147200\)	\(2.2715\)
189630.ey1	189630r4	\([1, -1, 1, -2285492, -1146957969]\)	\(15393836938735081/2275690697640\)	\(195177163732366654440\)	\([2]\)	\(8294400\)	\(2.6180\)

Rank

The elliptic curves in class 189630r have rank \(0\).

Complex multiplication

The elliptic curves in class 189630r do not have complex multiplication.

Modular form 189630.2.a.r

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.