Elliptic curve isogeny class with LMFDB label 17298.g (Cremona label 17298i)

• Label: 17298.g
• Number of curves: $4$
• Conductor: $17298$
• CM: no
• Rank: $1$

Elliptic curves in class 17298.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17298.g1	17298i4	\([1, -1, 0, -2860116, 1862474714]\)	\(3999236143617/62\)	\(40113391373838\)	\([2]\)	\(245760\)	\(2.1582\)
17298.g2	17298i3	\([1, -1, 0, -265416, -1869130]\)	\(3196010817/1847042\)	\(1195018042418007858\)	\([2]\)	\(245760\)	\(2.1582\)
17298.g3	17298i2	\([1, -1, 0, -178926, 29076992]\)	\(979146657/3844\)	\(2487030265177956\)	\([2, 2]\)	\(122880\)	\(1.8116\)
17298.g4	17298i1	\([1, -1, 0, -5946, 881252]\)	\(-35937/496\)	\(-320907130990704\)	\([2]\)	\(61440\)	\(1.4651\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 17298.g have rank \(1\).

Complex multiplication

The elliptic curves in class 17298.g do not have complex multiplication.

Modular form 17298.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.