Elliptic curve isogeny class with Cremona label 19890g (LMFDB label 19890.i)

• Label: 19890g
• Number of curves: $4$
• Conductor: $19890$
• CM: no
• Rank: $1$

Elliptic curves in class 19890g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19890.i4	19890g1	\([1, -1, 0, -2745, 11421]\)	\(3138428376721/1747933200\)	\(1274243302800\)	\([2]\)	\(24576\)	\(1.0131\)	\(\Gamma_0(N)\)-optimal
19890.i2	19890g2	\([1, -1, 0, -33165, 2329425]\)	\(5534056064805841/9890302500\)	\(7210030522500\)	\([2, 2]\)	\(49152\)	\(1.3597\)
19890.i1	19890g3	\([1, -1, 0, -530415, 148819275]\)	\(22638311752145721841/72499050\)	\(52851807450\)	\([2]\)	\(98304\)	\(1.7063\)
19890.i3	19890g4	\([1, -1, 0, -22635, 3826791]\)	\(-1759334717565361/7634341406250\)	\(-5565434885156250\)	\([2]\)	\(98304\)	\(1.7063\)

Rank

The elliptic curves in class 19890g have rank \(1\).

Complex multiplication

The elliptic curves in class 19890g do not have complex multiplication.

Modular form 19890.2.a.g

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.