Elliptic curve isogeny class with Cremona label 446160bo (LMFDB label 446160.bo)

• Label: 446160bo
• Number of curves: $4$
• Conductor: $446160$
• CM: no
• Rank: $0$

Elliptic curves in class 446160bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
446160.bo4	446160bo1	\([0, -1, 0, -1615696, 9097026496]\)	\(-23592983745241/1794399750000\)	\(-35476377038429184000000\)	\([2]\)	\(27869184\)	\(3.0066\)	\(\Gamma_0(N)\)-optimal^*
446160.bo3	446160bo2	\([0, -1, 0, -75975696, 253176290496]\)	\(2453170411237305241/19353090685500\)	\(382622401735014684672000\)	\([2]\)	\(55738368\)	\(3.3532\)	\(\Gamma_0(N)\)-optimal^*
446160.bo2	446160bo3	\([0, -1, 0, -383893696, 2895290653696]\)	\(-316472948332146183241/7074906009600\)	\(-139875205125289436774400\)	\([2]\)	\(83607552\)	\(3.5559\)	\(\Gamma_0(N)\)-optimal^*
446160.bo1	446160bo4	\([0, -1, 0, -6142332096, 185290371910656]\)	\(1296294060988412126189641/647824320\)	\(12807881761566228480\)	\([2]\)	\(167215104\)	\(3.9025\)	\(\Gamma_0(N)\)-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 446160bo1.

Rank

The elliptic curves in class 446160bo have rank \(0\).

Complex multiplication

The elliptic curves in class 446160bo do not have complex multiplication.

Modular form 446160.2.a.bo

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.