Elliptic curve isogeny class with Cremona label 485100he (LMFDB label 485100.he)

• Label: 485100he
• Number of curves: $4$
• Conductor: $485100$
• CM: no
• Rank: $1$

Elliptic curves in class 485100he

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
485100.he3	485100he1	\([0, 0, 0, -29341200, 62080041625]\)	\(-130287139815424/2250652635\)	\(-48257436555594708750000\)	\([2]\)	\(47775744\)	\(3.1505\)	\(\Gamma_0(N)\)-optimal^*
485100.he2	485100he2	\([0, 0, 0, -471388575, 3939277567750]\)	\(33766427105425744/9823275\)	\(3370016769065100000000\)	\([2]\)	\(95551488\)	\(3.4971\)	\(\Gamma_0(N)\)-optimal^*
485100.he4	485100he3	\([0, 0, 0, 113542800, 297499292125]\)	\(7549996227362816/6152409907875\)	\(-131917083150101525718750000\)	\([2]\)	\(143327232\)	\(3.6998\)
485100.he1	485100he4	\([0, 0, 0, -546799575, 2594830414750]\)	\(52702650535889104/22020583921875\)	\(7554480260536743187500000000\)	\([2]\)	\(286654464\)	\(4.0464\)

^*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 485100he1.

Rank

The elliptic curves in class 485100he have rank \(1\).

Complex multiplication

The elliptic curves in class 485100he do not have complex multiplication.

Modular form 485100.2.a.he

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.