Elliptic curve isogeny class with Cremona label 61710c (LMFDB label 61710.i)

• Label: 61710c
• Number of curves: $4$
• Conductor: $61710$
• CM: no
• Rank: $0$

Elliptic curves in class 61710c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61710.i3	61710c1	\([1, 1, 0, -12223, -459323]\)	\(114013572049/15667200\)	\(27755400499200\)	\([2]\)	\(245760\)	\(1.3063\)	\(\Gamma_0(N)\)-optimal
61710.i2	61710c2	\([1, 1, 0, -50943, 3947013]\)	\(8253429989329/936360000\)	\(1658818857960000\)	\([2, 2]\)	\(491520\)	\(1.6529\)
61710.i4	61710c3	\([1, 1, 0, 70057, 19991613]\)	\(21464092074671/109596256200\)	\(-194156453229928200\)	\([2]\)	\(983040\)	\(1.9995\)
61710.i1	61710c4	\([1, 1, 0, -791463, 270682317]\)	\(30949975477232209/478125000\)	\(847027603125000\)	\([2]\)	\(983040\)	\(1.9995\)

Rank

The elliptic curves in class 61710c have rank \(0\).

Complex multiplication

The elliptic curves in class 61710c do not have complex multiplication.

Modular form 61710.2.a.c

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.