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

• Label: 487872om
• Number of curves: $4$
• Conductor: $487872$
• CM: no
• Rank: $0$

Elliptic curves in class 487872om

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
487872.om4	487872om1	\([0, 0, 0, 120516, -637453168]\)	\(9148592/8301447\)	\(-175653730662009126912\)	\([2]\)	\(15728640\)	\(2.5636\)	\(\Gamma_0(N)\)-optimal^*
487872.om3	487872om2	\([0, 0, 0, -10421004, -12650569360]\)	\(1478729816932/38900169\)	\(3292418687119311568896\)	\([2, 2]\)	\(31457280\)	\(2.9102\)	\(\Gamma_0(N)\)-optimal^*
487872.om2	487872om3	\([0, 0, 0, -23837484, 26606051120]\)	\(8849350367426/3314597517\)	\(561079454706228654637056\)	\([2]\)	\(62914560\)	\(3.2567\)	\(\Gamma_0(N)\)-optimal^*
487872.om1	487872om4	\([0, 0, 0, -165668844, -820746626128]\)	\(2970658109581346/2139291\)	\(362129103633773887488\)	\([2]\)	\(62914560\)	\(3.2567\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 487872om1.

Rank

The elliptic curves in class 487872om have rank \(0\).

Complex multiplication

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

Modular form 487872.2.a.om

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.