Elliptic curve isogeny class with Cremona label 481650ge (LMFDB label 481650.ge)

• Label: 481650ge
• Number of curves: $4$
• Conductor: $481650$
• CM: no
• Rank: $0$

Elliptic curves in class 481650ge

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
481650.ge3	481650ge1	\([1, 1, 1, -109305063, 443846474781]\)	\(-1914980734749238129/20440940544000\)	\(-1541633059160064000000000\)	\([2]\)	\(149299200\)	\(3.4577\)	\(\Gamma_0(N)\)-optimal^*
481650.ge2	481650ge2	\([1, 1, 1, -1753337063, 28257579850781]\)	\(7903870428425797297009/886464000000\)	\(66856131459000000000000\)	\([2]\)	\(298598400\)	\(3.8042\)	\(\Gamma_0(N)\)-optimal^*
481650.ge4	481650ge3	\([1, 1, 1, 361190937, 2310807050781]\)	\(69096190760262356111/70568821500000000\)	\(-5322222230243648437500000000\)	\([2]\)	\(447897600\)	\(4.0070\)
481650.ge1	481650ge4	\([1, 1, 1, -1957151063, 21279481294781]\)	\(10993009831928446009969/3767761230468750000\)	\(284160372141838073730468750000\)	\([2]\)	\(895795200\)	\(4.3536\)

^*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 481650ge1.

Rank

The elliptic curves in class 481650ge have rank \(0\).

Complex multiplication

The elliptic curves in class 481650ge do not have complex multiplication.

Modular form 481650.2.a.ge

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.