Elliptic curves over $\Q$ of conductor 51800

Results (29 matches)

 

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
51800.a1	51800y1	51800.a	51800y	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{10} \cdot 5^{8} \cdot 7^{4} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$148$	$2$	$0$	$1$	$1$		$0$	$122880$	$1.337318$	$-793036420/88837$	$0.78925$	$3.72867$	$[0, 1, 0, -14208, -716912]$	\(y^2=x^3+x^2-14208x-716912\)	148.2.0.?	$[]$
51800.b1	51800s2	51800.b	51800s	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( 2^{11} \cdot 5^{6} \cdot 7^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$221184$	$1.496210$	$169556172914/4353013$	$0.88931$	$3.97394$	$[0, 1, 0, -36608, -2647712]$	\(y^2=x^3+x^2-36608x-2647712\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[]$
51800.b2	51800s1	51800.b	51800s	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{10} \cdot 5^{6} \cdot 7^{3} \cdot 37^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$110592$	$1.149635$	$415292/469567$	$0.92128$	$3.41791$	$[0, 1, 0, 392, -131712]$	\(y^2=x^3+x^2+392x-131712\)	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
51800.c1	51800e1	51800.c	51800e	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{3} \cdot 7 \cdot 37 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$0.692381446$	$1$		$12$	$4736$	$-0.181420$	$-1257728/259$	$0.63366$	$2.02210$	$[0, -1, 0, -28, 77]$	\(y^2=x^3-x^2-28x+77\)	2590.2.0.?	$[(2, 5), (-2, 11)]$
51800.d1	51800l1	51800.d	51800l	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{11} \cdot 5^{10} \cdot 7^{3} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2072$	$2$	$0$	$1$	$1$		$0$	$123840$	$1.447855$	$5191150/12691$	$0.78015$	$3.71734$	$[0, -1, 0, 9792, 666412]$	\(y^2=x^3-x^2+9792x+666412\)	2072.2.0.?	$[]$
51800.e1	51800k1	51800.e	51800k	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{7} \cdot 7 \cdot 37 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$1.228222442$	$1$		$12$	$13056$	$0.311885$	$-256/1295$	$0.73734$	$2.49193$	$[0, -1, 0, -8, -863]$	\(y^2=x^3-x^2-8x-863\)	2590.2.0.?	$[(12, 25), (32, 175)]$
51800.f1	51800w1	51800.f	51800w	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{8} \cdot 5^{9} \cdot 7 \cdot 37^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$3.388436900$	$1$		$2$	$174080$	$1.534315$	$-334932755456/9583$	$0.86477$	$4.28989$	$[0, -1, 0, -114833, -14939963]$	\(y^2=x^3-x^2-114833x-14939963\)	70.2.0.a.1	$[(467, 5750)]$
51800.g1	51800f1	51800.g	51800f	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{9} \cdot 7^{3} \cdot 37^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$1.358334202$	$1$		$2$	$224640$	$1.515965$	$25408728832/17373979$	$0.85554$	$3.79690$	$[0, -1, 0, 19292, 433037]$	\(y^2=x^3-x^2+19292x+433037\)	2590.2.0.?	$[(17, 875)]$
51800.h1	51800d1	51800.h	51800d	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{7} \cdot 7 \cdot 37^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$4.261645161$	$1$		$2$	$269568$	$1.685957$	$-24351951486578944/1772855$	$0.92048$	$4.62091$	$[0, -1, 0, -380408, -90180563]$	\(y^2=x^3-x^2-380408x-90180563\)	2590.2.0.?	$[(758, 7511)]$
51800.i1	51800n1	51800.i	51800n	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{8} \cdot 5^{7} \cdot 7^{11} \cdot 37^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$0.318895841$	$1$		$6$	$1351680$	$2.465439$	$3246125782016/13534801555835$	$1.01562$	$4.87259$	$[0, -1, 0, 48967, -354000563]$	\(y^2=x^3-x^2+48967x-354000563\)	70.2.0.a.1	$[(2447, 120050)]$
51800.j1	51800j1	51800.j	51800j	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{9} \cdot 7^{3} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$1$	$1$		$0$	$128640$	$1.375555$	$-1074343269632/12691$	$0.86206$	$4.14184$	$[0, -1, 0, -67208, -6683963]$	\(y^2=x^3-x^2-67208x-6683963\)	2590.2.0.?	$[]$
51800.k1	51800u1	51800.k	51800u	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{11} \cdot 5^{3} \cdot 7 \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10360$	$2$	$0$	$1.977848074$	$1$		$2$	$11648$	$0.187839$	$265302/259$	$0.76519$	$2.29767$	$[0, 0, 0, 85, -250]$	\(y^2=x^3+85x-250\)	10360.2.0.?	$[(10, 40)]$
51800.l1	51800g1	51800.l	51800g	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{11} \cdot 5^{9} \cdot 7 \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10360$	$2$	$0$	$1$	$1$		$0$	$58240$	$0.992558$	$265302/259$	$0.76519$	$3.18726$	$[0, 0, 0, 2125, -31250]$	\(y^2=x^3+2125x-31250\)	10360.2.0.?	$[]$
51800.m1	51800b1	51800.m	51800b	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( 2^{4} \cdot 5^{6} \cdot 7^{2} \cdot 37^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1036$	$12$	$0$	$4.958463167$	$1$		$1$	$195840$	$1.712460$	$33256413948450816/2481997$	$1.11932$	$4.64961$	$[0, 0, 0, -422050, -105534375]$	\(y^2=x^3-422050x-105534375\)	2.3.0.a.1, 28.6.0.c.1, 74.6.0.?, 1036.12.0.?	$[(26200/3, 4124575/3)]$
51800.m2	51800b2	51800.m	51800b	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{8} \cdot 5^{6} \cdot 7 \cdot 37^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1036$	$12$	$0$	$9.916926335$	$1$		$1$	$391680$	$2.059032$	$-2065624967846736/17960084863$	$1.06882$	$4.65041$	$[0, 0, 0, -421175, -105993750]$	\(y^2=x^3-421175x-105993750\)	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[(4427719/39, 9061838128/39)]$
51800.n1	51800p1	51800.n	51800p	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{8} \cdot 5^{6} \cdot 7 \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$518$	$2$	$0$	$1$	$1$		$0$	$20736$	$0.411097$	$27648/259$	$0.75618$	$2.59320$	$[0, 0, 0, 100, -1500]$	\(y^2=x^3+100x-1500\)	518.2.0.?	$[]$
51800.o1	51800q1	51800.o	51800q	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( 2^{4} \cdot 5^{6} \cdot 7^{2} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$16128$	$0.369806$	$6912000/1813$	$0.92588$	$2.59582$	$[0, 0, 0, -250, 1125]$	\(y^2=x^3-250x+1125\)	2.3.0.a.1, 28.6.0.c.1, 74.6.0.?, 1036.12.0.?	$[]$
51800.o2	51800q2	51800.o	51800q	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{8} \cdot 5^{6} \cdot 7 \cdot 37^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1036$	$12$	$0$	$1$	$1$		$1$	$32256$	$0.716380$	$6750000/9583$	$0.85629$	$2.88349$	$[0, 0, 0, 625, 7250]$	\(y^2=x^3+625x+7250\)	2.3.0.a.1, 14.6.0.b.1, 148.6.0.?, 1036.12.0.?	$[]$
51800.p1	51800c1	51800.p	51800c	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{8} \cdot 5^{6} \cdot 7^{7} \cdot 37^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$518$	$2$	$0$	$0.225312800$	$1$		$6$	$564480$	$2.178257$	$-15283295882302464/41714923579$	$1.00656$	$4.83384$	$[0, 0, 0, -820700, 286844500]$	\(y^2=x^3-820700x+286844500\)	518.2.0.?	$[(1074, 25382)]$
51800.q1	51800m1	51800.q	51800m	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{8} \cdot 5^{7} \cdot 7 \cdot 37^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$1.202106757$	$1$		$4$	$36864$	$0.853580$	$70575104/47915$	$0.75050$	$3.06527$	$[0, 1, 0, 1367, -7637]$	\(y^2=x^3+x^2+1367x-7637\)	70.2.0.a.1	$[(9, 74)]$
51800.r1	51800x1	51800.r	51800x	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{3} \cdot 7^{3} \cdot 37^{3} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$1.178693649$	$1$		$8$	$44928$	$0.711246$	$25408728832/17373979$	$0.85554$	$2.90731$	$[0, 1, 0, 772, 3773]$	\(y^2=x^3+x^2+772x+3773\)	2590.2.0.?	$[(23, 185), (22/3, 2035/3)]$
51800.s1	51800v1	51800.s	51800v	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{3} \cdot 7^{3} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$5.517820088$	$1$		$2$	$25728$	$0.570837$	$-1074343269632/12691$	$0.86206$	$3.25225$	$[0, 1, 0, -2688, -54547]$	\(y^2=x^3+x^2-2688x-54547\)	2590.2.0.?	$[(322, 5707)]$
51800.t1	51800z1	51800.t	51800z	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{9} \cdot 7 \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$1.253443273$	$1$		$2$	$23680$	$0.623299$	$-1257728/259$	$0.63366$	$2.91169$	$[0, 1, 0, -708, 8213]$	\(y^2=x^3+x^2-708x+8213\)	2590.2.0.?	$[(-17, 125)]$
51800.u1	51800h1	51800.u	51800h	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{11} \cdot 5^{4} \cdot 7^{3} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2072$	$2$	$0$	$1$	$1$		$0$	$24768$	$0.643137$	$5191150/12691$	$0.78015$	$2.82775$	$[0, 1, 0, 392, 5488]$	\(y^2=x^3+x^2+392x+5488\)	2072.2.0.?	$[]$
51800.v1	51800i1	51800.v	51800i	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{8} \cdot 5^{3} \cdot 7 \cdot 37^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$1$	$1$		$0$	$34816$	$0.729597$	$-334932755456/9583$	$0.86477$	$3.40030$	$[0, 1, 0, -4593, -121357]$	\(y^2=x^3+x^2-4593x-121357\)	70.2.0.a.1	$[]$
51800.w1	51800a1	51800.w	51800a	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{10} \cdot 5^{2} \cdot 7^{4} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$148$	$2$	$0$	$1$	$1$		$0$	$24576$	$0.532599$	$-793036420/88837$	$0.78925$	$2.83908$	$[0, -1, 0, -568, -5508]$	\(y^2=x^3-x^2-568x-5508\)	148.2.0.?	$[]$
51800.x1	51800r1	51800.x	51800r	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{11} \cdot 5^{7} \cdot 7^{3} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10360$	$2$	$0$	$1$	$1$		$0$	$135936$	$1.205544$	$-11683450802/63455$	$0.81210$	$3.72837$	$[0, -1, 0, -15008, 716012]$	\(y^2=x^3-x^2-15008x+716012\)	10360.2.0.?	$[]$
51800.y1	51800o1	51800.y	51800o	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{11} \cdot 7 \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$2.451711604$	$1$		$0$	$88320$	$0.857407$	$1029037824/809375$	$0.78108$	$3.05672$	$[0, 0, 0, 1325, -11125]$	\(y^2=x^3+1325x-11125\)	2590.2.0.?	$[(190/3, 4375/3)]$
51800.z1	51800t1	51800.z	51800t	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( - 2^{4} \cdot 5^{9} \cdot 7^{11} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2590$	$2$	$0$	$1$	$1$		$0$	$1343232$	$2.201710$	$1623525901056/9145136186375$	$1.04143$	$4.58106$	$[0, 0, 0, 15425, -72744625]$	\(y^2=x^3+15425x-72744625\)	2590.2.0.?	$[]$