Elliptic curve isogeny class with Cremona label 17850s (LMFDB label 17850.y)

• Label: 17850s
• Number of curves: $4$
• Conductor: $17850$
• CM: no
• Rank: $1$

Elliptic curves in class 17850s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17850.y4	17850s1	\([1, 0, 1, 24, 12598]\)	\(103823/4386816\)	\(-68544000000\)	\([2]\)	\(24576\)	\(0.75812\)	\(\Gamma_0(N)\)-optimal
17850.y3	17850s2	\([1, 0, 1, -7976, 268598]\)	\(3590714269297/73410624\)	\(1147041000000\)	\([2, 2]\)	\(49152\)	\(1.1047\)
17850.y2	17850s3	\([1, 0, 1, -16976, -451402]\)	\(34623662831857/14438442312\)	\(225600661125000\)	\([2]\)	\(98304\)	\(1.4513\)
17850.y1	17850s4	\([1, 0, 1, -126976, 17404598]\)	\(14489843500598257/6246072\)	\(97594875000\)	\([2]\)	\(98304\)	\(1.4513\)

Rank

The elliptic curves in class 17850s have rank \(1\).

Complex multiplication

The elliptic curves in class 17850s do not have complex multiplication.

Modular form 17850.2.a.s

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.