Elliptic curve isogeny class with Cremona label 90a (LMFDB label 90.a)

• Label: 90a
• Number of curves: $4$
• Conductor: $90$
• CM: no
• Rank: $0$

Elliptic curves in class 90a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
90.a4	90a1	\([1, -1, 0, 6, 0]\)	\(804357/500\)	\(-13500\)	\([6]\)	\(8\)	\(-0.51836\)	\(\Gamma_0(N)\)-optimal
90.a3	90a2	\([1, -1, 0, -24, 18]\)	\(57960603/31250\)	\(843750\)	\([6]\)	\(16\)	\(-0.17179\)
90.a2	90a3	\([1, -1, 0, -69, -235]\)	\(-1860867/320\)	\(-6298560\)	\([2]\)	\(24\)	\(0.030944\)
90.a1	90a4	\([1, -1, 0, -1149, -14707]\)	\(8527173507/200\)	\(3936600\)	\([2]\)	\(48\)	\(0.37752\)

Rank

The elliptic curves in class 90a have rank \(0\).

Complex multiplication

The elliptic curves in class 90a do not have complex multiplication.

Modular form 90.2.a.a

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.