LMFDB - Elliptic curves over $\Q$ of conductor 83582

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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

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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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
83582.a1	83582e1	83582.a	83582e	$1$	$1$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{4} \cdot 23^{8} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$		$0$	$709632$	$1.632151$	$1180597050009/668656$	$0.87299$	$4.11256$	$[1, -1, 0, -116479, -15264419]$	$y^2+xy=x^3-x^2-116479x-15264419$	316.2.0.?	$[]$
83582.b1	83582k1	83582.b	83582k	$1$	$1$	$ 2 \cdot 23^{2} \cdot 79 $	$ - 2^{5} \cdot 23^{7} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$14536$	$2$	$0$	$0.607281043$	$1$		$4$	$295680$	$1.161356$	$-389017/58144$	$0.90322$	$3.28601$	$[1, 0, 1, -805, 141360]$	$y^2+xy+y=x^3-805x+141360$	14536.2.0.?	$[(-48, 288)]$
83582.c1	83582i1	83582.c	83582i	$1$	$1$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{2} \cdot 23^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1.295522948$	$1$		$4$	$95040$	$0.797182$	$4826809/316$	$0.94063$	$3.01782$	$[1, 1, 0, -1862, -29912]$	$y^2+xy=x^3+x^2-1862x-29912$	316.2.0.?	$[(59, 235)]$
83582.d1	83582h2	83582.d	83582h	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2 \cdot 23^{3} \cdot 79^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$14536$	$12$	$0$	$3.697764403$	$1$		$2$	$28032$	$0.322276$	$206425071/12482$	$0.87397$	$2.51923$	$[1, -1, 0, -283, -1665]$	$y^2+xy=x^3-x^2-283x-1665$	2.3.0.a.1, 184.6.0.?, 632.6.0.?, 7268.6.0.?, 14536.12.0.?	$[(31, 121)]$
83582.d2	83582h1	83582.d	83582h	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{2} \cdot 23^{3} \cdot 79 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$14536$	$12$	$0$	$1.848882201$	$1$		$5$	$14016$	$-0.024297$	$1367631/316$	$0.72931$	$2.07658$	$[1, -1, 0, -53, 129]$	$y^2+xy=x^3-x^2-53x+129$	2.3.0.a.1, 184.6.0.?, 632.6.0.?, 3634.6.0.?, 14536.12.0.?	$[(8, 9)]$
83582.e1	83582g1	83582.e	83582g	$1$	$1$	$ 2 \cdot 23^{2} \cdot 79 $	$ - 2^{2} \cdot 23^{4} \cdot 79^{2} $	$3$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.2.0.1		$316$	$4$	$0$	$0.879885583$	$1$		$28$	$71424$	$0.576849$	$31379751/24964$	$0.85503$	$2.62968$	$[1, -1, 0, 430, 1992]$	$y^2+xy=x^3-x^2+430x+1992$	4.2.0.a.1, 316.4.0.?	$[(6, 66), (236, 3516), (29, 181)]$
83582.f1	83582f2	83582.f	83582f	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{8} \cdot 23^{3} \cdot 79^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.33	2B	$29072$	$96$	$3$	$1.460523977$	$1$		$4$	$205824$	$1.462713$	$208475114097375/9971220736$	$0.96451$	$3.73909$	$[1, -1, 0, -28412, 1772624]$	$y^2+xy=x^3-x^2-28412x+1772624$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.s.1, 16.24.0.k.1, 92.12.0.?, $\ldots$	$[(61, 483)]$
83582.f2	83582f1	83582.f	83582f	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ - 2^{16} \cdot 23^{3} \cdot 79^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.36	2B	$29072$	$96$	$3$	$2.921047955$	$1$		$3$	$102912$	$1.116140$	$9869198625/409010176$	$1.01896$	$3.23608$	$[1, -1, 0, 1028, 106320]$	$y^2+xy=x^3-x^2+1028x+106320$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.v.1, 16.24.0.n.2, 46.6.0.a.1, $\ldots$	$[(129, 1476)]$
83582.g1	83582a2	83582.g	83582a	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{8} \cdot 23^{9} \cdot 79^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.33	2B	$29072$	$96$	$3$	$1$	$1$		$0$	$4733952$	$3.030460$	$208475114097375/9971220736$	$0.96451$	$5.39902$	$[1, -1, 0, -15030047, -21477336115]$	$y^2+xy=x^3-x^2-15030047x-21477336115$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.s.1, 16.24.0.k.1, 92.12.0.?, $\ldots$	$[]$
83582.g2	83582a1	83582.g	83582a	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ - 2^{16} \cdot 23^{9} \cdot 79^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.36	2B	$29072$	$96$	$3$	$1$	$1$		$1$	$2366976$	$2.683887$	$9869198625/409010176$	$1.01896$	$4.89601$	$[1, -1, 0, 543713, -1296857907]$	$y^2+xy=x^3-x^2+543713x-1296857907$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.v.1, 16.24.0.n.2, 46.6.0.a.1, $\ldots$	$[]$
83582.h1	83582b1	83582.h	83582b	$1$	$1$	$ 2 \cdot 23^{2} \cdot 79 $	$ - 2^{2} \cdot 23^{10} \cdot 79^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.2.0.1		$7268$	$4$	$0$	$1$	$4$	$2$	$0$	$1642752$	$2.144596$	$31379751/24964$	$0.85503$	$4.28961$	$[1, -1, 0, 227371, -25601079]$	$y^2+xy=x^3-x^2+227371x-25601079$	4.2.0.a.1, 7268.4.0.?	$[]$
83582.i1	83582c2	83582.i	83582c	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2 \cdot 23^{9} \cdot 79^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$14536$	$12$	$0$	$23.53775319$	$1$		$4$	$644736$	$1.890024$	$206425071/12482$	$0.87397$	$4.17916$	$[1, -1, 0, -149806, 21156702]$	$y^2+xy=x^3-x^2-149806x+21156702$	2.3.0.a.1, 184.6.0.?, 632.6.0.?, 7268.6.0.?, 14536.12.0.?	$[(87, 2919), (3281/5, 233656/5)]$
83582.i2	83582c1	83582.i	83582c	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{2} \cdot 23^{9} \cdot 79 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$14536$	$12$	$0$	$23.53775319$	$1$		$7$	$322368$	$1.543449$	$1367631/316$	$0.72931$	$3.73651$	$[1, -1, 0, -28136, -1400916]$	$y^2+xy=x^3-x^2-28136x-1400916$	2.3.0.a.1, 184.6.0.?, 632.6.0.?, 3634.6.0.?, 14536.12.0.?	$[(-130, 282), (260, 2838)]$
83582.j1	83582d3	83582.j	83582d	$3$	$9$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{18} \cdot 23^{6} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$65412$	$144$	$3$	$5.631518876$	$1$		$4$	$1425600$	$2.247604$	$15698803397448457/20709376$	$1.00146$	$4.95036$	$[1, 0, 1, -2759540, 1764192370]$	$y^2+xy+y=x^3-2759540x+1764192370$	3.4.0.a.1, 9.12.0.a.1, 69.8.0-3.a.1.1, 207.24.0.?, 316.2.0.?, $\ldots$	$[(964, -218), (59569/9, 8127863/9)]$
83582.j2	83582d2	83582.j	83582d	$3$	$9$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{6} \cdot 23^{6} \cdot 79^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$65412$	$144$	$3$	$5.631518876$	$1$		$8$	$475200$	$1.698299$	$59914169497/31554496$	$0.96798$	$3.84955$	$[1, 0, 1, -43125, 1030080]$	$y^2+xy+y=x^3-43125x+1030080$	3.12.0.a.1, 69.24.0-3.a.1.1, 316.2.0.?, 711.36.0.?, 948.24.1.?, $\ldots$	$[(-117, 2174), (1470, 55074)]$
83582.j3	83582d1	83582.j	83582d	$3$	$9$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{2} \cdot 23^{6} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$65412$	$144$	$3$	$5.631518876$	$1$		$6$	$158400$	$1.148993$	$11134383337/316$	$0.90937$	$3.70106$	$[1, 0, 1, -24610, -1487960]$	$y^2+xy+y=x^3-24610x-1487960$	3.4.0.a.1, 9.12.0.a.1, 69.8.0-3.a.1.2, 207.24.0.?, 316.2.0.?, $\ldots$	$[(-91, 47), (182, 173)]$
83582.k1	83582j2	83582.k	83582j	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{19} \cdot 23^{12} \cdot 79^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$14536$	$12$	$0$	$207.0533228$	$1$		$0$	$75601152$	$3.960697$	$2470170476556066238923961/484385480113651712$	$1.06209$	$6.61567$	$[1, 1, 0, -1489784358, -22129511053420]$	$y^2+xy=x^3+x^2-1489784358x-22129511053420$	2.3.0.a.1, 8.6.0.b.1, 7268.6.0.?, 14536.12.0.?	$[(-675369689575815521527787823806454724389364755393592122363363780395336692979936935805473346215/174283843808206780090615036054265382499117289, 375642232067675915437653484132948514954546840452330664580750512165081507783075739587798293496459829536088545455637162267069872996156570600/174283843808206780090615036054265382499117289)]$
83582.k2	83582j1	83582.k	83582j	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{38} \cdot 23^{9} \cdot 79 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$14536$	$12$	$0$	$103.5266614$	$1$		$1$	$37800576$	$3.614124$	$817348184878300169401/264210720009224192$	$1.05146$	$5.90860$	$[1, 1, 0, -103042598, -267527207020]$	$y^2+xy=x^3+x^2-103042598x-267527207020$	2.3.0.a.1, 8.6.0.c.1, 3634.6.0.?, 14536.12.0.?	$[(162390575115927235974772511304666982901624408035/3285270208522661421161, 44422525479658318006932059133965990210372867177765647514059199274334550/3285270208522661421161)]$
83582.l1	83582m1	83582.l	83582m	$1$	$1$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{8} \cdot 23^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$0.884209214$	$1$		$4$	$402688$	$1.101170$	$72511713/20224$	$0.89606$	$3.25689$	$[1, -1, 1, -4596, -85161]$	$y^2+xy+y=x^3-x^2-4596x-85161$	316.2.0.?	$[(121, 997)]$
83582.m1	83582n2	83582.m	83582n	$2$	$5$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{4} \cdot 23^{6} \cdot 79^{5} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$36340$	$48$	$1$	$1.293984324$	$1$		$8$	$2851200$	$2.709858$	$1413378216646643521/49232902384$	$1.01962$	$5.34742$	$[1, 1, 1, -12368031, 16736019925]$	$y^2+xy+y=x^3+x^2-12368031x+16736019925$	5.12.0.a.2, 115.24.0.?, 316.2.0.?, 1580.24.1.?, 36340.48.1.?	$[(1949, 5266), (33949/4, 391771/4)]$
83582.m2	83582n1	83582.m	83582n	$2$	$5$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{20} \cdot 23^{6} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$36340$	$48$	$1$	$1.293984324$	$1$		$18$	$570240$	$1.905138$	$8194759433281/82837504$	$0.96131$	$4.28351$	$[1, 1, 1, -222191, -40051275]$	$y^2+xy+y=x^3+x^2-222191x-40051275$	5.12.0.a.1, 115.24.0.?, 316.2.0.?, 1580.24.1.?, 36340.48.1.?	$[(795, 16530), (-263, 660)]$
83582.n1	83582o1	83582.n	83582o	$1$	$1$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2^{14} \cdot 23^{8} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$		$0$	$1537536$	$1.966387$	$2105518942513/684703744$	$0.87228$	$4.16360$	$[1, 1, 1, -141254, 13465539]$	$y^2+xy+y=x^3+x^2-141254x+13465539$	316.2.0.?	$[]$
83582.o1	83582l1	83582.o	83582l	$1$	$1$	$ 2 \cdot 23^{2} \cdot 79 $	$ - 2 \cdot 23^{9} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$14536$	$2$	$0$	$15.31479709$	$1$		$0$	$379776$	$1.547321$	$-4657463/158$	$0.74984$	$3.84966$	$[1, 1, 1, -42331, 3431467]$	$y^2+xy+y=x^3+x^2-42331x+3431467$	14536.2.0.?	$[(-279795659/1236, 4428972105311/1236)]$
83582.p1	83582p1	83582.p	83582p	$1$	$1$	$ 2 \cdot 23^{2} \cdot 79 $	$ - 2 \cdot 23^{3} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$14536$	$2$	$0$	$1$	$1$		$0$	$16512$	$-0.020426$	$-4657463/158$	$0.74984$	$2.18972$	$[1, 1, 1, -80, -317]$	$y^2+xy+y=x^3+x^2-80x-317$	14536.2.0.?	$[]$
83582.q1	83582q2	83582.q	83582q	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ 2 \cdot 23^{6} \cdot 79^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$632$	$12$	$0$	$1$	$9$	$3$	$0$	$152064$	$1.077282$	$81182737/12482$	$0.85973$	$3.26686$	$[1, 1, 1, -4772, -110717]$	$y^2+xy+y=x^3+x^2-4772x-110717$	2.3.0.a.1, 8.6.0.b.1, 316.6.0.?, 632.12.0.?	$[]$
83582.q2	83582q1	83582.q	83582q	$2$	$2$	$ 2 \cdot 23^{2} \cdot 79 $	$ - 2^{2} \cdot 23^{6} \cdot 79 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$632$	$12$	$0$	$1$	$9$	$3$	$1$	$76032$	$0.730708$	$103823/316$	$0.80009$	$2.80693$	$[1, 1, 1, 518, -9149]$	$y^2+xy+y=x^3+x^2+518x-9149$	2.3.0.a.1, 8.6.0.c.1, 158.6.0.?, 632.12.0.?	$[]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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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