Elliptic curve isogeny class with Cremona label 485520hh (LMFDB label 485520.hh)

• Label: 485520hh
• Number of curves: $2$
• Conductor: $485520$
• CM: no
• Rank: $0$

Elliptic curves in class 485520hh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
485520.hh2	485520hh1	\([0, 1, 0, 4135146000, 422644925812500]\)	\(16098893047132187167/168182866341984375\)	\(-81692463033035576231541696000000\)	\([2]\)	\(1102970880\)	\(4.8044\)	\(\Gamma_0(N)\)-optimal^*
485520.hh1	485520hh2	\([0, 1, 0, -65490710880, 5991014605304628]\)	\(63953244990201015504593/5088175635498046875\)	\(2471509786040266227291000000000000\)	\([2]\)	\(2205941760\)	\(5.1510\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 485520hh1.

Rank

The elliptic curves in class 485520hh have rank \(0\).

Complex multiplication

The elliptic curves in class 485520hh do not have complex multiplication.

Modular form 485520.2.a.hh

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.