Elliptic curve isogeny class with LMFDB label 443982.bl (Cremona label 443982bl)

• Label: 443982.bl
• Number of curves: $4$
• Conductor: $443982$
• CM: no
• Rank: $1$

Elliptic curves in class 443982.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
443982.bl1	443982bl4	\([1, 1, 1, -13581833, 19258728257]\)	\(312196988566716625/25367712678\)	\(22513938380275367718\)	\([2]\)	\(17625600\)	\(2.7585\)	\(\Gamma_0(N)\)-optimal^*
443982.bl2	443982bl3	\([1, 1, 1, -790923, 343530549]\)	\(-61653281712625/21875235228\)	\(-19414351787590874268\)	\([2]\)	\(8812800\)	\(2.4120\)	\(\Gamma_0(N)\)-optimal^*
443982.bl3	443982bl2	\([1, 1, 1, -348863, -39923827]\)	\(5290763640625/2291573592\)	\(2033779998182392152\)	\([2]\)	\(5875200\)	\(2.2092\)	\(\Gamma_0(N)\)-optimal^*
443982.bl4	443982bl1	\([1, 1, 1, 73977, -4574403]\)	\(50447927375/39517632\)	\(-35072043864403392\)	\([2]\)	\(2937600\)	\(1.8627\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 443982.bl1.

Rank

The elliptic curves in class 443982.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 443982.bl do not have complex multiplication.

Modular form 443982.2.a.bl

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.