Elliptic curve isogeny class with Cremona label 499800hj (LMFDB label 499800.hj)

• Label: 499800hj
• Number of curves: $4$
• Conductor: $499800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 499800hj have rank \(0\).

Complex multiplication

The elliptic curves in class 499800hj do not have complex multiplication.

Modular form 499800.2.a.hj

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.

Elliptic curves in class 499800hj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
499800.hj4	499800hj1	\([0, 1, 0, -865639308, -9894245486112]\)	\(-152435594466395827792/1646846627220711\)	\(-774999435383557713756000000\)	\([2]\)	\(212336640\)	\(3.9755\)	\(\Gamma_0(N)\)-optimal^*
499800.hj3	499800hj2	\([0, 1, 0, -13885943808, -629816983340112]\)	\(157304700372188331121828/18069292138401\)	\(34013346412651827984000000\)	\([2, 2]\)	\(424673280\)	\(4.3221\)	\(\Gamma_0(N)\)-optimal^*
499800.hj2	499800hj3	\([0, 1, 0, -13921664808, -626413772228112]\)	\(79260902459030376659234/842751810121431609\)	\(3172765046687241835751712000000\)	\([2]\)	\(849346560\)	\(4.6687\)	\(\Gamma_0(N)\)-optimal^*
499800.hj1	499800hj4	\([0, 1, 0, -222175094808, -40308067092236112]\)	\(322159999717985454060440834/4250799\)	\(16003272049632000000\)	\([2]\)	\(849346560\)	\(4.6687\)

^*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 499800hj1.