LMFDB - Elliptic curves over $\Q$ of conductor 1666

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (26 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1666.a1	1666h1	1666.a	1666h	$1$	$1$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{26} \cdot 7^{10} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$68$	$2$	$0$	$5.820922052$	$1$	$0$	$43680$	$2.042763$	$-164384733177/1140850688$	$1.05960$	$6.45023$	$[1, -1, 0, -74881, -28409795]$	$y^2+xy=x^3-x^2-74881x-28409795$	68.2.0.a.1	$[(19602/7, 738305/7)]$
1666.b1	1666g2	1666.b	1666g	$2$	$2$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2^{5} \cdot 7^{8} \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$56$	$12$	$0$	$0.461090677$	$1$	$10$	$7680$	$1.220789$	$234770924809/130960928$	$0.97956$	$5.10332$	$[1, 0, 1, -6298, 36012]$	$y^2+xy+y=x^3-6298x+36012$	2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1	$[(-24, 428)]$
1666.b2	1666g1	1666.b	1666g	$2$	$2$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{10} \cdot 7^{7} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$56$	$12$	$0$	$0.922181354$	$1$	$9$	$3840$	$0.874216$	$3449795831/2071552$	$0.94689$	$4.53441$	$[1, 0, 1, 1542, 4652]$	$y^2+xy+y=x^3+1542x+4652$	2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1	$[(29, 257)]$
1666.c1	1666b1	1666.c	1666b	$2$	$3$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2 \cdot 7^{8} \cdot 17 $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$408$	$16$	$0$	$3.236389112$	$1$	$4$	$840$	$0.318712$	$-208537/34$	$0.76885$	$3.78305$	$[1, 0, 1, -222, 1418]$	$y^2+xy+y=x^3-222x+1418$	3.8.0-3.a.1.2, 136.2.0.?, 408.16.0.?	$[(-16, 38)]$
1666.c2	1666b2	1666.c	1666b	$2$	$3$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{3} \cdot 7^{8} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$408$	$16$	$0$	$1.078796370$	$1$	$4$	$2520$	$0.868018$	$63905303/39304$	$0.92407$	$4.52135$	$[1, 0, 1, 1493, -5442]$	$y^2+xy+y=x^3+1493x-5442$	3.8.0-3.a.1.1, 136.2.0.?, 408.16.0.?	$[(4, 22)]$
1666.d1	1666a1	1666.d	1666a	$1$	$1$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{2} \cdot 7^{8} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$68$	$2$	$0$	$0.441794610$	$1$	$6$	$672$	$0.361417$	$-208537/68$	$0.77633$	$3.80984$	$[1, 1, 0, -221, -1679]$	$y^2+xy=x^3+x^2-221x-1679$	68.2.0.a.1	$[(20, 39)]$
1666.e1	1666d2	1666.e	1666d	$2$	$2$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2 \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$952$	$12$	$0$	$1.035388955$	$1$	$6$	$768$	$0.521677$	$60698457/28322$	$0.89781$	$3.98978$	$[1, -1, 0, -401, -1261]$	$y^2+xy=x^3-x^2-401x-1261$	2.3.0.a.1, 8.6.0.b.1, 476.6.0.?, 952.12.0.?	$[(-5, 27)]$
1666.e2	1666d1	1666.e	1666d	$2$	$2$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{2} \cdot 7^{7} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$952$	$12$	$0$	$2.070777910$	$1$	$5$	$384$	$0.175103$	$658503/476$	$0.89406$	$3.37996$	$[1, -1, 0, 89, -183]$	$y^2+xy=x^3-x^2+89x-183$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(4, 13)]$
1666.f1	1666e1	1666.f	1666e	$1$	$1$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{2} \cdot 7^{2} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$68$	$2$	$0$	$0.313271241$	$1$	$4$	$96$	$-0.611538$	$-208537/68$	$0.77633$	$2.23594$	$[1, 0, 1, -5, 4]$	$y^2+xy+y=x^3-5x+4$	68.2.0.a.1	$[(1, 0)]$
1666.g1	1666f1	1666.g	1666f	$2$	$3$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2 \cdot 7^{2} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2856$	$16$	$0$	$1.542807845$	$1$	$2$	$120$	$-0.654243$	$-208537/34$	$0.76885$	$2.20915$	$[1, 1, 0, -4, -6]$	$y^2+xy=x^3+x^2-4x-6$	3.4.0.a.1, 21.8.0-3.a.1.1, 136.2.0.?, 408.8.0.?, 2856.16.0.?	$[(3, 3)]$
1666.g2	1666f2	1666.g	1666f	$2$	$3$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{3} \cdot 7^{2} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2856$	$16$	$0$	$0.514269281$	$1$	$2$	$360$	$-0.104937$	$63905303/39304$	$0.92407$	$2.94745$	$[1, 1, 0, 31, 29]$	$y^2+xy=x^3+x^2+31x+29$	3.4.0.a.1, 21.8.0-3.a.1.2, 136.2.0.?, 408.8.0.?, 2856.16.0.?	$[(7, 22)]$
1666.h1	1666c1	1666.h	1666c	$1$	$1$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{26} \cdot 7^{4} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$68$	$2$	$0$	$2.144168461$	$1$	$0$	$6240$	$1.069809$	$-164384733177/1140850688$	$1.05960$	$4.87633$	$[1, -1, 0, -1528, 83264]$	$y^2+xy=x^3-x^2-1528x+83264$	68.2.0.a.1	$[(-464/3, 4792/3)]$
1666.i1	1666n2	1666.i	1666n	$2$	$2$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2 \cdot 7^{10} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$136$	$12$	$0$	$1$	$1$	$0$	$1536$	$0.841352$	$2433138625/1387778$	$0.96221$	$4.48734$	$[1, 0, 0, -1373, -2465]$	$y^2+xy=x^3-1373x-2465$	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[]$
1666.i2	1666n1	1666.i	1666n	$2$	$2$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2^{2} \cdot 7^{8} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$136$	$12$	$0$	$1$	$1$	$1$	$768$	$0.494778$	$647214625/3332$	$0.86431$	$4.30883$	$[1, 0, 0, -883, 9981]$	$y^2+xy=x^3-883x+9981$	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[]$
1666.j1	1666k3	1666.j	1666k	$4$	$4$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2 \cdot 7^{8} \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.15	2B	$952$	$48$	$0$	$2.100298289$	$1$	$0$	$3072$	$1.252085$	$16342588257633/8185058$	$1.11945$	$5.67528$	$[1, -1, 1, -25906, 1610655]$	$y^2+xy+y=x^3-x^2-25906x+1610655$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 28.12.0-4.c.1.1, 56.24.0-8.k.1.1, $\ldots$	$[(351/2, 331/2)]$
1666.j2	1666k2	1666.j	1666k	$4$	$4$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2^{2} \cdot 7^{10} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.3	2Cs	$952$	$48$	$0$	$4.200596579$	$1$	$4$	$1536$	$0.905511$	$6403769793/2775556$	$1.13395$	$4.61779$	$[1, -1, 1, -1896, 16391]$	$y^2+xy+y=x^3-x^2-1896x+16391$	2.6.0.a.1, 8.12.0.a.1, 28.12.0-2.a.1.1, 56.24.0-8.a.1.2, 68.12.0.b.1, $\ldots$	$[(81, 583)]$
1666.j3	1666k1	1666.j	1666k	$4$	$4$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2^{4} \cdot 7^{8} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$952$	$48$	$0$	$2.100298289$	$1$	$5$	$768$	$0.558937$	$721734273/13328$	$0.89265$	$4.32352$	$[1, -1, 1, -916, -10265]$	$y^2+xy+y=x^3-x^2-916x-10265$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 28.12.0-4.c.1.2, 34.6.0.a.1, $\ldots$	$[(-17, 21)]$
1666.j4	1666k4	1666.j	1666k	$4$	$4$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2 \cdot 7^{14} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$952$	$48$	$0$	$8.401193158$	$1$	$0$	$3072$	$1.252085$	$250404380127/196003234$	$0.98833$	$5.11201$	$[1, -1, 1, 6434, 116351]$	$y^2+xy+y=x^3-x^2+6434x+116351$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 56.24.0-8.p.1.2, 136.24.0.?, $\ldots$	$[(2083/6, 171743/6)]$
1666.k1	1666i1	1666.k	1666i	$1$	$1$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{13} \cdot 7^{8} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$0.226115444$	$1$	$8$	$2184$	$0.963688$	$1296351/139264$	$1.08366$	$4.69936$	$[1, -1, 1, 407, -43095]$	$y^2+xy+y=x^3-x^2+407x-43095$	136.2.0.?	$[(135, 1500)]$
1666.l1	1666j1	1666.l	1666j	$1$	$1$	$ 2 \cdot 7^{2} \cdot 17 $	$ - 2^{13} \cdot 7^{2} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$0.168287453$	$1$	$6$	$312$	$-0.009267$	$1296351/139264$	$1.08366$	$3.12547$	$[1, -1, 1, 8, 123]$	$y^2+xy+y=x^3-x^2+8x+123$	136.2.0.?	$[(-3, 9)]$
1666.m1	1666l4	1666.m	1666l	$4$	$6$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2 \cdot 7^{6} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$2856$	$96$	$1$	$1$	$1$	$0$	$3456$	$1.152443$	$159661140625/48275138$	$1.06848$	$5.05134$	$[1, 1, 1, -5538, 107309]$	$y^2+xy+y=x^3+x^2-5538x+107309$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 21.8.0-3.a.1.2, $\ldots$	$[]$
1666.m2	1666l3	1666.m	1666l	$4$	$6$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2^{2} \cdot 7^{6} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$2856$	$96$	$1$	$1$	$1$	$1$	$1728$	$0.805869$	$120920208625/19652$	$0.98564$	$5.01388$	$[1, 1, 1, -5048, 135925]$	$y^2+xy+y=x^3+x^2-5048x+135925$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 21.8.0-3.a.1.2, $\ldots$	$[]$
1666.m3	1666l2	1666.m	1666l	$4$	$6$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2^{3} \cdot 7^{6} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$2856$	$96$	$1$	$1$	$1$	$0$	$1152$	$0.603136$	$8805624625/2312$	$0.96590$	$4.66073$	$[1, 1, 1, -2108, -38123]$	$y^2+xy+y=x^3+x^2-2108x-38123$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 21.8.0-3.a.1.1, $\ldots$	$[]$
1666.m4	1666l1	1666.m	1666l	$4$	$6$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 7^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$2856$	$96$	$1$	$1$	$1$	$1$	$576$	$0.256563$	$3048625/1088$	$0.90010$	$3.58655$	$[1, 1, 1, -148, -491]$	$y^2+xy+y=x^3+x^2-148x-491$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 21.8.0-3.a.1.1, $\ldots$	$[]$
1666.n1	1666m2	1666.n	1666m	$2$	$2$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2^{7} \cdot 7^{10} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$136$	$12$	$0$	$1$	$1$	$0$	$10752$	$1.378401$	$37936442980801/88817792$	$0.95838$	$5.78880$	$[1, 1, 1, -34301, -2454509]$	$y^2+xy+y=x^3+x^2-34301x-2454509$	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[]$
1666.n2	1666m1	1666.n	1666m	$2$	$2$	$ 2 \cdot 7^{2} \cdot 17 $	$ 2^{14} \cdot 7^{8} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$136$	$12$	$0$	$1$	$1$	$1$	$5376$	$1.031826$	$23912763841/13647872$	$0.98171$	$4.79540$	$[1, 1, 1, -2941, -8429]$	$y^2+xy+y=x^3+x^2-2941x-8429$	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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