LMFDB - Elliptic curves over $\Q$ of conductor 83259

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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 (28 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
83259.a1	83259i1	83259.a	83259i	$1$	$1$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{10} \cdot 11 \cdot 29^{2} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1.128386198$	$1$		$12$	$42240$	$0.358085$	$118784/891$	$0.80314$	$2.42663$	$[0, 0, 1, 87, 1080]$	$y^2+y=x^3+87x+1080$	22.2.0.a.1	$[(5, 40), (-1, 31)]$
83259.b1	83259m3	83259.b	83259m	$3$	$25$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{6} \cdot 11 \cdot 29^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.60.0.2	5B.4.2	$47850$	$1200$	$37$	$3.765703940$	$1$		$0$	$3780000$	$2.729664$	$-52893159101157376/11$	$1.09296$	$5.76383$	$[0, 0, 1, -59192103, 175284602712]$	$y^2+y=x^3-59192103x+175284602712$	5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 110.24.1.?, 275.300.12.?, $\ldots$	$[(70905/4, 76499/4)]$
83259.b2	83259m2	83259.b	83259m	$3$	$25$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{6} \cdot 11^{5} \cdot 29^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.60.0.1	5Cs.4.1	$47850$	$1200$	$37$	$0.753140788$	$1$		$4$	$756000$	$1.924944$	$-122023936/161051$	$1.01300$	$4.11336$	$[0, 0, 1, -78213, 15249222]$	$y^2+y=x^3-78213x+15249222$	5.60.0.a.1, 22.2.0.a.1, 110.120.5.?, 275.300.12.?, 435.120.0.?, $\ldots$	$[(-87, 4625)]$
83259.b3	83259m1	83259.b	83259m	$3$	$25$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{6} \cdot 11 \cdot 29^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.60.0.1	5B.4.1	$47850$	$1200$	$37$	$3.765703940$	$1$		$2$	$151200$	$1.120226$	$-4096/11$	$0.82546$	$3.25191$	$[0, 0, 1, -2523, -115848]$	$y^2+y=x^3-2523x-115848$	5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 110.24.1.?, 275.300.12.?, $\ldots$	$[(1218, 42470)]$
83259.c1	83259b2	83259.c	83259b	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{3} \cdot 11 \cdot 29^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3828$	$12$	$0$	$4.192192077$	$1$		$0$	$779520$	$1.679773$	$21647657403/9251$	$0.91346$	$4.17467$	$[1, -1, 1, -146492, -21536210]$	$y^2+xy+y=x^3-x^2-146492x-21536210$	2.3.0.a.1, 66.6.0.a.1, 348.6.0.?, 1276.6.0.?, 3828.12.0.?	$[(8347/3, 670358/3)]$
83259.c2	83259b1	83259.c	83259b	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{3} \cdot 11^{2} \cdot 29^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3828$	$12$	$0$	$2.096096038$	$1$		$3$	$389760$	$1.333199$	$-3176523/3509$	$0.93171$	$3.48982$	$[1, -1, 1, -7727, -443930]$	$y^2+xy+y=x^3-x^2-7727x-443930$	2.3.0.a.1, 132.6.0.?, 174.6.0.?, 1276.6.0.?, 3828.12.0.?	$[(892, 26045)]$
83259.d1	83259g1	83259.d	83259g	$1$	$1$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{6} \cdot 11 \cdot 29^{2} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$4.353773475$	$1$		$6$	$11760$	$-0.008940$	$783/11$	$0.71531$	$2.04214$	$[1, -1, 1, 16, 118]$	$y^2+xy+y=x^3-x^2+16x+118$	22.2.0.a.1	$[(-1, 10), (2, 11)]$
83259.e1	83259a2	83259.e	83259a	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{9} \cdot 11^{2} \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$9.797730817$	$1$		$0$	$580608$	$1.744263$	$19034163/121$	$0.94120$	$4.13541$	$[1, -1, 1, -126308, -17151236]$	$y^2+xy+y=x^3-x^2-126308x-17151236$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.?	$[(250921/17, 110663830/17)]$
83259.e2	83259a1	83259.e	83259a	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{9} \cdot 11 \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$4.898865408$	$1$		$1$	$290304$	$1.397690$	$19683/11$	$1.13667$	$3.52867$	$[1, -1, 1, -12773, 106084]$	$y^2+xy+y=x^3-x^2-12773x+106084$	2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.?	$[(-2176/5, 98308/5)]$
83259.f1	83259e2	83259.f	83259e	$2$	$3$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{8} \cdot 11^{3} \cdot 29^{2} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1914$	$16$	$0$	$1.656310964$	$1$		$10$	$103680$	$1.091642$	$-2390367404032/11979$	$1.07897$	$3.69195$	$[0, 0, 1, -23664, 1401142]$	$y^2+y=x^3-23664x+1401142$	3.4.0.a.1, 22.2.0.a.1, 66.8.0.a.1, 87.8.0.?, 1914.16.0.?	$[(88, 13), (94, 85)]$
83259.f2	83259e1	83259.f	83259e	$2$	$3$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{12} \cdot 11 \cdot 29^{2} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1914$	$16$	$0$	$1.656310964$	$1$		$8$	$34560$	$0.542336$	$-950272/8019$	$0.89943$	$2.63351$	$[0, 0, 1, -174, 3487]$	$y^2+y=x^3-174x+3487$	3.4.0.a.1, 22.2.0.a.1, 66.8.0.a.1, 87.8.0.?, 1914.16.0.?	$[(25, 121), (13, 58)]$
83259.g1	83259n2	83259.g	83259n	$2$	$3$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{8} \cdot 11^{3} \cdot 29^{8} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$66$	$16$	$0$	$1$	$1$		$2$	$3006720$	$2.775291$	$-2390367404032/11979$	$1.07897$	$5.47521$	$[0, 0, 1, -19901424, 34172458335]$	$y^2+y=x^3-19901424x+34172458335$	3.8.0-3.a.1.2, 22.2.0.a.1, 66.16.0-66.a.1.4	$[]$
83259.g2	83259n1	83259.g	83259n	$2$	$3$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{12} \cdot 11 \cdot 29^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$66$	$16$	$0$	$1$	$1$		$0$	$1002240$	$2.225986$	$-950272/8019$	$0.89943$	$4.41676$	$[0, 0, 1, -146334, 85050540]$	$y^2+y=x^3-146334x+85050540$	3.8.0-3.a.1.1, 22.2.0.a.1, 66.16.0-66.a.1.1	$[]$
83259.h1	83259j1	83259.h	83259j	$1$	$1$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{7} \cdot 11^{2} \cdot 29^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$6$	$2$	$0$	$4.166547919$	$1$		$2$	$584640$	$1.994959$	$-950272/363$	$0.80174$	$4.21912$	$[0, 0, 1, -146334, 27760779]$	$y^2+y=x^3-146334x+27760779$	6.2.0.a.1	$[(-361, 5791)]$
83259.i1	83259k1	83259.i	83259k	$1$	$1$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{7} \cdot 11^{2} \cdot 29^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$6$	$2$	$0$	$0.372547764$	$1$		$4$	$20160$	$0.311310$	$-950272/363$	$0.80174$	$2.43586$	$[0, 0, 1, -174, 1138]$	$y^2+y=x^3-174x+1138$	6.2.0.a.1	$[(16, 49)]$
83259.j1	83259d2	83259.j	83259d	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{3} \cdot 11^{2} \cdot 29^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$0$	$193536$	$1.194958$	$19034163/121$	$0.94120$	$3.55361$	$[1, -1, 0, -14034, 639909]$	$y^2+xy=x^3-x^2-14034x+639909$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.?	$[]$
83259.j2	83259d1	83259.j	83259d	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{3} \cdot 11 \cdot 29^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$96768$	$0.848384$	$19683/11$	$1.13667$	$2.94686$	$[1, -1, 0, -1419, -3456]$	$y^2+xy=x^3-x^2-1419x-3456$	2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.?	$[]$
83259.k1	83259f1	83259.k	83259f	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{13} \cdot 11 \cdot 29^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3828$	$12$	$0$	$1$	$9$	$3$	$1$	$1881600$	$2.534138$	$13132563308857/20231937$	$0.92296$	$5.03116$	$[1, -1, 0, -3720321, -2757359880]$	$y^2+xy=x^3-x^2-3720321x-2757359880$	2.3.0.a.1, 66.6.0.a.1, 116.6.0.?, 3828.12.0.?	$[]$
83259.k2	83259f2	83259.k	83259f	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{20} \cdot 11^{2} \cdot 29^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3828$	$12$	$0$	$1$	$9$	$3$	$0$	$3763200$	$2.880711$	$-4601630708137/16783438221$	$0.94815$	$5.11408$	$[1, -1, 0, -2622816, -4417445943]$	$y^2+xy=x^3-x^2-2622816x-4417445943$	2.3.0.a.1, 116.6.0.?, 132.6.0.?, 3828.12.0.?	$[]$
83259.l1	83259o1	83259.l	83259o	$1$	$1$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{6} \cdot 11 \cdot 29^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1$	$4$	$2$	$0$	$341040$	$1.674707$	$783/11$	$0.71531$	$3.82539$	$[1, -1, 0, 13719, 2980412]$	$y^2+xy=x^3-x^2+13719x+2980412$	22.2.0.a.1	$[]$
83259.m1	83259l4	83259.m	83259l	$4$	$4$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{9} \cdot 11^{4} \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$7656$	$48$	$0$	$8.801226149$	$1$		$0$	$1161216$	$2.220322$	$347873904937/395307$	$1.00913$	$4.71067$	$[1, -1, 0, -1109016, -448807311]$	$y^2+xy=x^3-x^2-1109016x-448807311$	2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 88.12.0.?, 116.12.0.?, $\ldots$	$[(-686685/34, -748083/34)]$
83259.m2	83259l2	83259.m	83259l	$4$	$4$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{12} \cdot 11^{2} \cdot 29^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3828$	$48$	$0$	$17.60245229$	$1$		$2$	$580608$	$1.873749$	$169112377/88209$	$1.00669$	$4.03731$	$[1, -1, 0, -87201, -3091608]$	$y^2+xy=x^3-x^2-87201x-3091608$	2.6.0.a.1, 12.12.0.a.1, 44.12.0.b.1, 116.12.0.?, 132.24.0.?, $\ldots$	$[(-206790821/2090, 9014446417737/2090)]$
83259.m3	83259l1	83259.m	83259l	$4$	$4$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{9} \cdot 11 \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$7656$	$48$	$0$	$8.801226149$	$1$		$1$	$290304$	$1.527174$	$30664297/297$	$1.09706$	$3.88660$	$[1, -1, 0, -49356, 4197339]$	$y^2+xy=x^3-x^2-49356x+4197339$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 66.6.0.a.1, 88.12.0.?, $\ldots$	$[(111547/38, 48206047/38)]$
83259.m4	83259l3	83259.m	83259l	$4$	$4$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{18} \cdot 11 \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$7656$	$48$	$0$	$35.20490459$	$1$		$0$	$1161216$	$2.220322$	$9090072503/5845851$	$1.03763$	$4.38898$	$[1, -1, 0, 329094, -24322653]$	$y^2+xy=x^3-x^2+329094x-24322653$	2.3.0.a.1, 4.6.0.c.1, 22.6.0.a.1, 24.12.0.ba.1, 44.12.0.g.1, $\ldots$	$[(54426284225127571/2731630, 12661174953393166585144491/2731630)]$
83259.n1	83259c2	83259.n	83259c	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ 3^{9} \cdot 11 \cdot 29^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3828$	$12$	$0$	$1$	$9$	$3$	$0$	$2338560$	$2.229080$	$21647657403/9251$	$0.91346$	$4.75647$	$[1, -1, 0, -1318425, 582796088]$	$y^2+xy=x^3-x^2-1318425x+582796088$	2.3.0.a.1, 66.6.0.a.1, 348.6.0.?, 1276.6.0.?, 3828.12.0.?	$[]$
83259.n2	83259c1	83259.n	83259c	$2$	$2$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{9} \cdot 11^{2} \cdot 29^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3828$	$12$	$0$	$1$	$9$	$3$	$1$	$1169280$	$1.882505$	$-3176523/3509$	$0.93171$	$4.07163$	$[1, -1, 0, -69540, 12055643]$	$y^2+xy=x^3-x^2-69540x+12055643$	2.3.0.a.1, 132.6.0.?, 174.6.0.?, 1276.6.0.?, 3828.12.0.?	$[]$
83259.o1	83259p1	83259.o	83259p	$1$	$1$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{10} \cdot 11 \cdot 29^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1$	$1$		$0$	$1224960$	$2.041733$	$118784/891$	$0.80314$	$4.20989$	$[0, 0, 1, 73167, 26346217]$	$y^2+y=x^3+73167x+26346217$	22.2.0.a.1	$[]$
83259.p1	83259h1	83259.p	83259h	$1$	$1$	$ 3^{2} \cdot 11 \cdot 29^{2} $	$ - 3^{6} \cdot 11 \cdot 29^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1$	$9$	$3$	$0$	$1081920$	$1.890196$	$-5601816576/9251$	$0.88114$	$4.34651$	$[0, 0, 1, -280053, 57125135]$	$y^2+y=x^3-280053x+57125135$	22.2.0.a.1	$[]$

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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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