Elliptic curve isogeny class with LMFDB label 418950.jk (Cremona label 418950jk)

• Label: 418950.jk
• Number of curves: $4$
• Conductor: $418950$
• CM: no
• Rank: $1$

Elliptic curves in class 418950.jk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418950.jk1	418950jk3	\([1, -1, 1, -186429305, -698276963303]\)	\(19804628171203875/5638671302656\)	\(204021688453378080768000000\)	\([2]\)	\(191102976\)	\(3.7550\)	\(\Gamma_0(N)\)-optimal^*
418950.jk2	418950jk1	\([1, -1, 1, -171122930, -861566572303]\)	\(11165451838341046875/572244736\)	\(28402321336452000000\)	\([2]\)	\(63700992\)	\(3.2057\)	\(\Gamma_0(N)\)-optimal^*
418950.jk3	418950jk2	\([1, -1, 1, -170828930, -864674740303]\)	\(-11108001800138902875/79947274872976\)	\(-3968036834708286600750000\)	\([2]\)	\(127401984\)	\(3.5523\)
418950.jk4	418950jk4	\([1, -1, 1, 490946695, -4606736483303]\)	\(361682234074684125/462672528510976\)	\(-16740686839351633921728000000\)	\([2]\)	\(382205952\)	\(4.1016\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 418950.jk1.

Rank

The elliptic curves in class 418950.jk have rank \(1\).

Complex multiplication

The elliptic curves in class 418950.jk do not have complex multiplication.

Modular form 418950.2.a.jk

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.