Elliptic curve isogeny class with LMFDB label 471510.ep (Cremona label 471510ep)

• Label: 471510.ep
• Number of curves: $6$
• Conductor: $471510$
• CM: no
• Rank: $1$

Elliptic curves in class 471510.ep

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
471510.ep1	471510ep5	[1, -1, 1, -467737952, 3893723161319]	[2]	62914560	\(\Gamma_0(N)\)-optimal^*
471510.ep2	471510ep3	[1, -1, 1, -29233652, 60844775879]	[2, 2]	31457280	\(\Gamma_0(N)\)-optimal^*
471510.ep3	471510ep6	[1, -1, 1, -28777352, 62835704039]	[2]	62914560
471510.ep4	471510ep4	[1, -1, 1, -5627732, -4005018169]	[2]	31457280
471510.ep5	471510ep2	[1, -1, 1, -1855652, 919809479]	[2, 2]	15728640	\(\Gamma_0(N)\)-optimal^*
471510.ep6	471510ep1	[1, -1, 1, 91228, 60067271]	[2]	7864320	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 471510.ep1.

Rank

The elliptic curves in class 471510.ep have rank \(1\).

Complex multiplication

The elliptic curves in class 471510.ep do not have complex multiplication.

Modular form 471510.2.a.ep

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.