Elliptic curve isogeny class with LMFDB label 198198.db (Cremona label 198198k)

• Label: 198198.db
• Number of curves: $4$
• Conductor: $198198$
• CM: no
• Rank: $1$

Elliptic curves in class 198198.db

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198198.db1	198198k3	\([1, -1, 1, -454136, 117906077]\)	\(8020417344913/187278\)	\(241863538298382\)	\([2]\)	\(1966080\)	\(1.8722\)
198198.db2	198198k2	\([1, -1, 1, -29426, 1705421]\)	\(2181825073/298116\)	\(385007265046404\)	\([2, 2]\)	\(983040\)	\(1.5257\)
198198.db3	198198k1	\([1, -1, 1, -7646, -228643]\)	\(38272753/4368\)	\(5641132088592\)	\([2]\)	\(491520\)	\(1.1791\)	\(\Gamma_0(N)\)-optimal
198198.db4	198198k4	\([1, -1, 1, 46804, 9023501]\)	\(8780064047/32388174\)	\(-41828289295398606\)	\([2]\)	\(1966080\)	\(1.8722\)

Rank

The elliptic curves in class 198198.db have rank \(1\).

Complex multiplication

The elliptic curves in class 198198.db do not have complex multiplication.

Modular form 198198.2.a.db

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.