Elliptic curves over $\Q$ of conductor 10005

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (25 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	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	Manin constant
10005.a1	10005k1	10005.a	10005k	$1$	$1$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{9} \cdot 5^{5} \cdot 23 \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20010$	$2$	$0$	$0.841750110$	$1$		$4$	$38880$	$1.187117$	$3511697101967355904/41026753125$	$0.94848$	$4.63613$	$[0, 1, 1, -31666, -2179460]$	\(y^2+y=x^3+x^2-31666x-2179460\)	20010.2.0.?	$[(-103, 4)]$	$1$
10005.b1	10005h2	10005.b	10005h	$2$	$2$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{2} \cdot 5^{4} \cdot 23^{2} \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2668$	$12$	$0$	$0.285535232$	$1$		$10$	$5888$	$0.501294$	$290656902035521/86293125$	$0.88440$	$3.61565$	$[1, 1, 1, -1380, 19152]$	\(y^2+xy+y=x^3+x^2-1380x+19152\)	2.3.0.a.1, 58.6.0.a.1, 92.6.0.?, 2668.12.0.?	$[(22, -4)]$	$1$
10005.b2	10005h1	10005.b	10005h	$2$	$2$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( - 3^{4} \cdot 5^{2} \cdot 23 \cdot 29^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2668$	$12$	$0$	$0.571070465$	$1$		$7$	$2944$	$0.154720$	$-46694890801/39169575$	$0.82606$	$2.76444$	$[1, 1, 1, -75, 360]$	\(y^2+xy+y=x^3+x^2-75x+360\)	2.3.0.a.1, 46.6.0.a.1, 116.6.0.?, 2668.12.0.?	$[(-2, 23)]$	$1$
10005.c1	10005f1	10005.c	10005f	$2$	$2$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3 \cdot 5^{2} \cdot 23 \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$40020$	$12$	$0$	$1.130966506$	$1$		$5$	$2048$	$-0.265641$	$7088952961/50025$	$0.78758$	$2.46251$	$[1, 1, 1, -40, 80]$	\(y^2+xy+y=x^3+x^2-40x+80\)	2.3.0.a.1, 20.6.0.b.1, 4002.6.0.?, 40020.12.0.?	$[(4, 0)]$	$1$
10005.c2	10005f2	10005.c	10005f	$2$	$2$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( - 3^{2} \cdot 5 \cdot 23^{2} \cdot 29^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$40020$	$12$	$0$	$0.565483253$	$1$		$8$	$4096$	$0.080932$	$-374805361/20020005$	$0.84818$	$2.63578$	$[1, 1, 1, -15, 210]$	\(y^2+xy+y=x^3+x^2-15x+210\)	2.3.0.a.1, 20.6.0.a.1, 8004.6.0.?, 40020.12.0.?	$[(0, 14)]$	$1$
10005.d1	10005e3	10005.d	10005e	$4$	$4$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3 \cdot 5^{3} \cdot 23 \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$80040$	$48$	$0$	$6.562466036$	$4$	$2$	$2$	$49152$	$1.711998$	$262537424941059264096001/250125$	$1.01946$	$5.85448$	$[1, 1, 1, -1334000, -593592940]$	\(y^2+xy+y=x^3+x^2-1334000x-593592940\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.1, 40.24.0-40.ba.1.2, $\ldots$	$[(1403, 16588)]$	$1$
10005.d2	10005e2	10005.d	10005e	$4$	$4$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{2} \cdot 5^{6} \cdot 23^{2} \cdot 29^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$40020$	$48$	$0$	$3.281233018$	$1$		$6$	$24576$	$1.365425$	$64096096056024006001/62562515625$	$0.95193$	$4.95144$	$[1, 1, 1, -83375, -9300940]$	\(y^2+xy+y=x^3+x^2-83375x-9300940\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.a.1.2, 8004.24.0.?, 40020.48.0.?	$[(678, 15358)]$	$1$
10005.d3	10005e4	10005.d	10005e	$4$	$4$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( - 3^{4} \cdot 5^{3} \cdot 23^{4} \cdot 29^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$80040$	$48$	$0$	$1.640616509$	$1$		$4$	$49152$	$1.711998$	$-62665433378363916001/2004003001000125$	$0.95242$	$4.95483$	$[1, 1, 1, -82750, -9446440]$	\(y^2+xy+y=x^3+x^2-82750x-9446440\)	2.3.0.a.1, 4.12.0-4.c.1.2, 20.24.0-20.h.1.1, 16008.24.0.?, 80040.48.0.?	$[(398, 4368)]$	$1$
10005.d4	10005e1	10005.d	10005e	$4$	$4$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3 \cdot 5^{12} \cdot 23 \cdot 29 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$80040$	$48$	$0$	$6.562466036$	$1$		$3$	$12288$	$1.018852$	$16003198512756001/488525390625$	$0.91071$	$4.05083$	$[1, 1, 1, -5250, -144690]$	\(y^2+xy+y=x^3+x^2-5250x-144690\)	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.ba.1.4, 4002.6.0.?, 8004.24.0.?, $\ldots$	$[(-3857/9, 8252/9)]$	$1$
10005.e1	10005a1	10005.e	10005a	$1$	$1$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{3} \cdot 5 \cdot 23 \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20010$	$2$	$0$	$0.908072202$	$1$		$4$	$1632$	$-0.210038$	$14959673344/90045$	$0.80703$	$2.54359$	$[0, -1, 1, -51, -124]$	\(y^2+y=x^3-x^2-51x-124\)	20010.2.0.?	$[(-4, 0)]$	$1$
10005.f1	10005b1	10005.f	10005b	$1$	$1$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3 \cdot 5^{5} \cdot 23^{3} \cdot 29^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20010$	$2$	$0$	$0.440061521$	$1$		$2$	$84000$	$1.987009$	$25101212833837967048704/2339617030153125$	$1.00166$	$5.59962$	$[0, -1, 1, -609991, 183560811]$	\(y^2+y=x^3-x^2-609991x+183560811\)	20010.2.0.?	$[(405, 1667)]$	$1$
10005.g1	10005m1	10005.g	10005m	$1$	$1$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{7} \cdot 5^{3} \cdot 23 \cdot 29^{13} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20010$	$2$	$0$	$8.613946887$	$1$		$2$	$2140320$	$3.644524$	$125147927114815865709295304704/64514985611316331088611125$	$1.08913$	$7.27396$	$[0, 1, 1, -104207741, 135268278965]$	\(y^2+y=x^3+x^2-104207741x+135268278965\)	20010.2.0.?	$[(-7253, 713854)]$	$1$
10005.h1	10005i2	10005.h	10005i	$2$	$3$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{5} \cdot 5^{15} \cdot 23^{3} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$20010$	$16$	$0$	$6.026588428$	$1$		$0$	$194400$	$2.427292$	$1489157481162281146384384/2616603057861328125$	$1.07366$	$6.04291$	$[0, 1, 1, -2379061, -1411043480]$	\(y^2+y=x^3+x^2-2379061x-1411043480\)	3.8.0-3.a.1.1, 20010.16.0.?	$[(-3451/2, 1931/2)]$	$1$
10005.h2	10005i1	10005.h	10005i	$2$	$3$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{15} \cdot 5^{5} \cdot 23 \cdot 29^{3} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$20010$	$16$	$0$	$2.008862809$	$1$		$6$	$64800$	$1.877985$	$210966209738334797824/25153051046653125$	$1.05362$	$5.08078$	$[0, 1, 1, -124021, 14938111]$	\(y^2+y=x^3+x^2-124021x+14938111\)	3.8.0-3.a.1.2, 20010.16.0.?	$[(-181, 5611)]$	$1$
10005.i1	10005l1	10005.i	10005l	$1$	$1$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( - 3^{6} \cdot 5^{4} \cdot 23^{7} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1334$	$2$	$0$	$1.149133118$	$1$		$4$	$349440$	$2.552017$	$-131631542171643599790505984/44988384234391875$	$1.02764$	$6.52949$	$[0, 1, 1, -10597711, -13282563134]$	\(y^2+y=x^3+x^2-10597711x-13282563134\)	1334.2.0.?	$[(6632, 456262)]$	$1$
10005.j1	10005n1	10005.j	10005n	$1$	$1$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3 \cdot 5^{3} \cdot 23^{5} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20010$	$2$	$0$	$1$	$1$		$0$	$6720$	$0.787657$	$245973316796416/69995230125$	$0.93654$	$3.59753$	$[0, 1, 1, -1305, 12506]$	\(y^2+y=x^3+x^2-1305x+12506\)	20010.2.0.?	$[ ]$	$1$
10005.k1	10005d4	10005.k	10005d	$4$	$4$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{2} \cdot 5 \cdot 23 \cdot 29^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$26680$	$48$	$0$	$6.375067733$	$1$		$2$	$7680$	$0.785313$	$18778886261717401/732035835$	$0.91105$	$4.06820$	$[1, 1, 0, -5537, 156294]$	\(y^2+xy=x^3+x^2-5537x+156294\)	2.3.0.a.1, 4.12.0-4.c.1.1, 232.24.0.?, 460.24.0.?, 26680.48.0.?	$[(655/2, 14679/2)]$	$1$
10005.k2	10005d3	10005.k	10005d	$4$	$4$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{2} \cdot 5^{4} \cdot 23^{4} \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$26680$	$48$	$0$	$1.593766933$	$1$		$4$	$7680$	$0.785313$	$512787603508921/45649063125$	$0.89026$	$3.67728$	$[1, 1, 0, -1667, -24804]$	\(y^2+xy=x^3+x^2-1667x-24804\)	2.3.0.a.1, 4.12.0-4.c.1.2, 58.6.0.a.1, 116.24.0.?, 920.24.0.?, $\ldots$	$[(-28, 44)]$	$1$
10005.k3	10005d2	10005.k	10005d	$4$	$4$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{4} \cdot 5^{2} \cdot 23^{2} \cdot 29^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$13340$	$48$	$0$	$3.187533866$	$1$		$4$	$3840$	$0.438739$	$5268932332201/900900225$	$0.85803$	$3.18026$	$[1, 1, 0, -362, 2079]$	\(y^2+xy=x^3+x^2-362x+2079\)	2.6.0.a.1, 4.12.0-2.a.1.1, 116.24.0.?, 460.24.0.?, 13340.48.0.?	$[(158, 1901)]$	$1$
10005.k4	10005d1	10005.k	10005d	$4$	$4$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( - 3^{8} \cdot 5 \cdot 23 \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$26680$	$48$	$0$	$6.375067733$	$1$		$1$	$1920$	$0.092165$	$8477185319/21880935$	$0.82352$	$2.61670$	$[1, 1, 0, 43, 216]$	\(y^2+xy=x^3+x^2+43x+216\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 116.12.0.?, 232.24.0.?, $\ldots$	$[(-135/8, 6183/8)]$	$1$
10005.l1	10005g2	10005.l	10005g	$2$	$2$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{6} \cdot 5^{8} \cdot 23^{2} \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2668$	$12$	$0$	$2.668730558$	$1$		$2$	$66048$	$1.528225$	$157264717208387436361/4368589453125$	$0.95575$	$5.04888$	$[1, 1, 0, -112452, -14561001]$	\(y^2+xy=x^3+x^2-112452x-14561001\)	2.3.0.a.1, 58.6.0.a.1, 92.6.0.?, 2668.12.0.?	$[(1338, 46581)]$	$1$
10005.l2	10005g1	10005.l	10005g	$2$	$2$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( - 3^{12} \cdot 5^{4} \cdot 23 \cdot 29^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2668$	$12$	$0$	$5.337461116$	$1$		$1$	$33024$	$1.181652$	$-33974761330806841/6424789539375$	$0.91815$	$4.16326$	$[1, 1, 0, -6747, -248544]$	\(y^2+xy=x^3+x^2-6747x-248544\)	2.3.0.a.1, 46.6.0.a.1, 116.6.0.?, 2668.12.0.?	$[(2957/4, 135171/4)]$	$1$
10005.m1	10005j1	10005.m	10005j	$2$	$2$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3^{3} \cdot 5^{2} \cdot 23 \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$40020$	$12$	$0$	$1.420687301$	$1$		$3$	$1728$	$0.132029$	$5763259856089/450225$	$0.85441$	$3.18999$	$[1, 0, 1, -374, 2747]$	\(y^2+xy+y=x^3-374x+2747\)	2.3.0.a.1, 20.6.0.b.1, 4002.6.0.?, 40020.12.0.?	$[(15, 16)]$	$1$
10005.m2	10005j2	10005.m	10005j	$2$	$2$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( - 3^{6} \cdot 5 \cdot 23^{2} \cdot 29^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$40020$	$12$	$0$	$0.710343650$	$1$		$4$	$3456$	$0.478603$	$-4681768588489/1621620405$	$0.86047$	$3.21836$	$[1, 0, 1, -349, 3137]$	\(y^2+xy+y=x^3-349x+3137\)	2.3.0.a.1, 20.6.0.a.1, 8004.6.0.?, 40020.12.0.?	$[(-5, 71)]$	$1$
10005.n1	10005c1	10005.n	10005c	$1$	$1$	\( 3 \cdot 5 \cdot 23 \cdot 29 \)	\( 3 \cdot 5^{3} \cdot 23 \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20010$	$2$	$0$	$2.812690896$	$1$		$0$	$1440$	$-0.272238$	$481890304/250125$	$0.84989$	$2.17062$	$[0, -1, 1, -16, -3]$	\(y^2+y=x^3-x^2-16x-3\)	20010.2.0.?	$[(-3/2, 19/2)]$	$1$

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