Elliptic curve isogeny class with Cremona label 222530r (LMFDB label 222530.bt)

• Label: 222530r
• Number of curves: $4$
• Conductor: $222530$
• CM: no
• Rank: $1$

Elliptic curves in class 222530r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
222530.bt4	222530r1	\([1, 1, 1, 2884, 488413]\)	\(109902239/4312000\)	\(-104081197528000\)	\([2]\)	\(884736\)	\(1.3695\)	\(\Gamma_0(N)\)-optimal
222530.bt2	222530r2	\([1, 1, 1, -78036, 7997789]\)	\(2177286259681/105875000\)	\(2555565117875000\)	\([2]\)	\(1769472\)	\(1.7161\)
222530.bt3	222530r3	\([1, 1, 1, -26016, -13337347]\)	\(-80677568161/3131816380\)	\(-75594433967580220\)	\([2]\)	\(2654208\)	\(1.9188\)
222530.bt1	222530r4	\([1, 1, 1, -1017286, -393192011]\)	\(4823468134087681/30382271150\)	\(733354166259834350\)	\([2]\)	\(5308416\)	\(2.2654\)

Rank

The elliptic curves in class 222530r have rank \(1\).

Complex multiplication

The elliptic curves in class 222530r do not have complex multiplication.

Modular form 222530.2.a.r

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.