Elliptic curve isogeny class with Cremona label 197106r (LMFDB label 197106.bi)

• Label: 197106r
• Number of curves: $4$
• Conductor: $197106$
• CM: no
• Rank: $1$

Elliptic curves in class 197106r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
197106.bi3	197106r1	\([1, 1, 1, -20404, 1082357]\)	\(19968681097/628992\)	\(29591482781952\)	\([2]\)	\(663552\)	\(1.3597\)	\(\Gamma_0(N)\)-optimal
197106.bi2	197106r2	\([1, 1, 1, -49284, -2706699]\)	\(281397674377/96589584\)	\(4544142074703504\)	\([2, 2]\)	\(1327104\)	\(1.7063\)
197106.bi4	197106r3	\([1, 1, 1, 145656, -18613803]\)	\(7264187703863/7406095788\)	\(-348426301116849228\)	\([2]\)	\(2654208\)	\(2.0529\)
197106.bi1	197106r4	\([1, 1, 1, -706304, -228721579]\)	\(828279937799497/193444524\)	\(9100768056205644\)	\([2]\)	\(2654208\)	\(2.0529\)

Rank

The elliptic curves in class 197106r have rank \(1\).

Complex multiplication

The elliptic curves in class 197106r do not have complex multiplication.

Modular form 197106.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.