Elliptic curve isogeny class with LMFDB label 487872.ii (Cremona label 487872ii)

• Label: 487872.ii
• Number of curves: $4$
• Conductor: $487872$
• CM: no
• Rank: $1$

Elliptic curves in class 487872.ii

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
487872.ii1	487872ii4	\([0, 0, 0, -985015020, -11898217435984]\)	\(312196988566716625/25367712678\)	\(8588253821778581515665408\)	\([2]\)	\(106168320\)	\(3.8295\)
487872.ii2	487872ii3	\([0, 0, 0, -57361260, -212377490512]\)	\(-61653281712625/21875235228\)	\(-7405873558009259473502208\)	\([2]\)	\(53084160\)	\(3.4830\)
487872.ii3	487872ii2	\([0, 0, 0, -25301100, 24568279472]\)	\(5290763640625/2291573592\)	\(775813567001205053325312\)	\([2]\)	\(35389440\)	\(3.2802\)	\(\Gamma_0(N)\)-optimal^*
487872.ii4	487872ii1	\([0, 0, 0, 5365140, 2844315056]\)	\(50447927375/39517632\)	\(-13378717204802281930752\)	\([2]\)	\(17694720\)	\(2.9337\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 487872.ii1.

Rank

The elliptic curves in class 487872.ii have rank \(1\).

Complex multiplication

The elliptic curves in class 487872.ii do not have complex multiplication.

Modular form 487872.2.a.ii

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.