Elliptic curve isogeny class with Cremona label 491970be (LMFDB label 491970.be)

• Label: 491970be
• Number of curves: $4$
• Conductor: $491970$
• CM: no
• Rank: $0$

Elliptic curves in class 491970be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
491970.be3	491970be1	\([1, 0, 1, -128823, -17805494]\)	\(1597099875769/186000\)	\(27534675354000\)	\([2]\)	\(3548160\)	\(1.6052\)	\(\Gamma_0(N)\)-optimal^*
491970.be2	491970be2	\([1, 0, 1, -139403, -14711902]\)	\(2023804595449/540562500\)	\(80022650247562500\)	\([2, 2]\)	\(7096320\)	\(1.9518\)	\(\Gamma_0(N)\)-optimal^*
491970.be1	491970be3	\([1, 0, 1, -800653, 263806598]\)	\(383432500775449/18701300250\)	\(2768463607964672250\)	\([2]\)	\(14192640\)	\(2.2983\)	\(\Gamma_0(N)\)-optimal^*
491970.be4	491970be4	\([1, 0, 1, 352567, -95198194]\)	\(32740359775271/45410156250\)	\(-6722332850097656250\)	\([2]\)	\(14192640\)	\(2.2983\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 491970be1.

Rank

The elliptic curves in class 491970be have rank \(0\).

Complex multiplication

The elliptic curves in class 491970be do not have complex multiplication.

Modular form 491970.2.a.be

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.