Elliptic curve isogeny class with Cremona label 439530cy (LMFDB label 439530.cy)

• Label: 439530cy
• Number of curves: $8$
• Conductor: $439530$
• CM: no
• Rank: $1$

Elliptic curves in class 439530cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
439530.cy7	439530cy1	\([1, 1, 1, -8224334931, -289200198054447]\)	\(-522923112164227281987660878881/4484275679769919488000000\)	\(-527570549449251257843712000000\)	\([2]\)	\(913047552\)	\(4.5283\)	\(\Gamma_0(N)\)-optimal^*
439530.cy6	439530cy2	\([1, 1, 1, -131859002451, -18429521516859951]\)	\(2155087111607167363355460545287201/156481162929000000000000\)	\(18409852337433921000000000000\)	\([2, 2]\)	\(1826095104\)	\(4.8749\)	\(\Gamma_0(N)\)-optimal^*
439530.cy8	439530cy3	\([1, 1, 1, 25178769069, -1530820093004847]\)	\(15005102139088880168192111025119/17288486242801155608083603200\)	\(-2033973117979313156135427832876800\)	\([2]\)	\(2739142656\)	\(5.0776\)	\(\Gamma_0(N)\)-optimal^*
439530.cy5	439530cy4	\([1, 1, 1, -132128682771, -18350351681061807]\)	\(2168337038351679228688694521765921/18360082088470458984375000000\)	\(2160045297626461029052734375000000\)	\([2]\)	\(3652190208\)	\(5.2215\)	\(\Gamma_0(N)\)-optimal^*
439530.cy2	439530cy5	\([1, 1, 1, -2109744002451, -1179486783062859951]\)	\(8827236347661221188886967161105287201/46539238473000000\)	\(5475294867109977000000\)	\([2]\)	\(3652190208\)	\(5.2215\)
439530.cy4	439530cy6	\([1, 1, 1, -145111052451, -14500978407039951]\)	\(2872347286043717137884962530087201/890114999660918118510786090000\)	\(104721139595107355724675472702410000\)	\([2, 2]\)	\(5478285312\)	\(5.4242\)	\(\Gamma_0(N)\)-optimal^*
439530.cy3	439530cy7	\([1, 1, 1, -905027120271, 320294635659563193]\)	\(696819431300451649932999125896765921/26551778102890598266349123437500\)	\(3123790142026975995437708023298437500\)	\([2]\)	\(10956570624\)	\(5.7708\)	\(\Gamma_0(N)\)-optimal^*
439530.cy1	439530cy8	\([1, 1, 1, -2109832128951, -1179383318775459351]\)	\(8828342566147309471108534663879471201/1536341563898865415843582949700\)	\(180749048651137617308581690449255300\)	\([2]\)	\(10956570624\)	\(5.7708\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 6 curves highlighted, and conditionally curve 439530cy1.

Rank

The elliptic curves in class 439530cy have rank \(1\).

Complex multiplication

The elliptic curves in class 439530cy do not have complex multiplication.

Modular form 439530.2.a.cy

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.