Elliptic curve isogeny class with LMFDB label 422370.dw (Cremona label 422370dw)

• Label: 422370.dw
• Number of curves: $6$
• Conductor: $422370$
• CM: no
• Rank: $0$

Elliptic curves in class 422370.dw

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
422370.dw1	422370dw6	[1, -1, 1, -29289803, -61005726943]	[2]	28311552
422370.dw2	422370dw3	[1, -1, 1, -2745473, 1750254581]	[2]	14155776	\(\Gamma_0(N)\)-optimal^*
422370.dw3	422370dw4	[1, -1, 1, -1835753, -947247163]	[2, 2]	14155776
422370.dw4	422370dw5	[1, -1, 1, -373703, -2415730183]	[2]	28311552
422370.dw5	422370dw2	[1, -1, 1, -211253, 13807037]	[2, 2]	7077888	\(\Gamma_0(N)\)-optimal^*
422370.dw6	422370dw1	[1, -1, 1, 48667, 1642781]	[2]	3538944	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 422370.dw6.

Rank

The elliptic curves in class 422370.dw have rank \(0\).

Modular form 422370.2.a.dw

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.