Elliptic curve isogeny class with Cremona label 130130i (LMFDB label 130130.i)

• Label: 130130i
• Number of curves: $4$
• Conductor: $130130$
• CM: no
• Rank: $1$

Elliptic curves in class 130130i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
130130.i3	130130i1	\([1, 0, 1, -451403, 35166198]\)	\(2107441550633329/1108665958400\)	\(5351318825998745600\)	\([2]\)	\(3773952\)	\(2.2853\)	\(\Gamma_0(N)\)-optimal
130130.i4	130130i2	\([1, 0, 1, 1711797, 274848758]\)	\(114926649504265871/73262465436160\)	\(-353623927529446013440\)	\([2]\)	\(7547904\)	\(2.6319\)
130130.i1	130130i3	\([1, 0, 1, -20839563, -36617683594]\)	\(207362104287019679089/5934929000000\)	\(28646768711561000000\)	\([2]\)	\(11321856\)	\(2.8346\)
130130.i2	130130i4	\([1, 0, 1, -19994563, -39722889594]\)	\(-183146792453150159089/35223382235041000\)	\(-170016538382536014169000\)	\([2]\)	\(22643712\)	\(3.1812\)

Rank

The elliptic curves in class 130130i have rank \(1\).

Complex multiplication

The elliptic curves in class 130130i do not have complex multiplication.

Modular form 130130.2.a.i

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.