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 proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 471510.ep6.

Rank

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

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.