Elliptic curves over $\Q$ of conductor 16731

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

Results (28 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	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
16731.a1	16731m3	16731.a	16731m	$3$	$25$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{6} \cdot 11 \cdot 13^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.2	5B.4.2	$21450$	$1200$	$37$	$3.186265103$	$1$		$0$	$324000$	$2.328491$	$-52893159101157376/11$	$1.09296$	$6.21988$	$[0, 0, 1, -11894727, 15789916444]$	\(y^2+y=x^3-11894727x+15789916444\)	5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 110.24.1.?, 195.24.0.?, $\ldots$	$[(199121/10, -331/10)]$	$1$
16731.a2	16731m2	16731.a	16731m	$3$	$25$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{6} \cdot 11^{5} \cdot 13^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.60.0.1	5Cs.4.1	$21450$	$1200$	$37$	$0.637253020$	$1$		$4$	$64800$	$1.523771$	$-122023936/161051$	$1.01300$	$4.29708$	$[0, 0, 1, -15717, 1373674]$	\(y^2+y=x^3-15717x+1373674\)	5.60.0.a.1, 22.2.0.a.1, 110.120.5.?, 195.120.0.?, 275.300.12.?, $\ldots$	$[(104, 929)]$	$1$
16731.a3	16731m1	16731.a	16731m	$3$	$25$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{6} \cdot 11 \cdot 13^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.1	5B.4.1	$21450$	$1200$	$37$	$3.186265103$	$1$		$2$	$12960$	$0.719052$	$-4096/11$	$0.82546$	$3.29348$	$[0, 0, 1, -507, -10436]$	\(y^2+y=x^3-507x-10436\)	5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 110.24.1.?, 195.24.0.?, $\ldots$	$[(299, 5154)]$	$1$
16731.b1	16731b2	16731.b	16731b	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{9} \cdot 11^{2} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1.454741438$	$1$		$6$	$55296$	$1.343090$	$19034163/121$	$0.94120$	$4.32276$	$[1, -1, 1, -25382, -1541510]$	\(y^2+xy+y=x^3-x^2-25382x-1541510\)	2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.?	$[(-94, 131)]$	$1$
16731.b2	16731b1	16731.b	16731b	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{9} \cdot 11 \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$2.909482877$	$1$		$5$	$27648$	$0.996516$	$19683/11$	$1.13667$	$3.61590$	$[1, -1, 1, -2567, 9910]$	\(y^2+xy+y=x^3-x^2-2567x+9910\)	2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.?	$[(76, 461)]$	$1$
16731.c1	16731h3	16731.c	16731h	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{8} \cdot 11 \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.93	2B	$6864$	$192$	$1$	$1$	$16$	$2$	$0$	$344064$	$2.372875$	$35765103905346817/1287$	$0.98956$	$6.17964$	$[1, -1, 1, -10440176, -12981429340]$	\(y^2+xy+y=x^3-x^2-10440176x-12981429340\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.5, 48.48.0-48.g.1.20, 132.12.0.?, $\ldots$	$[ ]$	$1$
16731.c2	16731h5	16731.c	16731h	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{7} \cdot 11^{8} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.94	2B	$6864$	$192$	$1$	$1$	$1$		$0$	$688128$	$2.719452$	$3013001140430737/108679952667$	$0.97853$	$5.92524$	$[1, -1, 1, -4576721, 3650404502]$	\(y^2+xy+y=x^3-x^2-4576721x+3650404502\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.3, 12.12.0.h.1, 24.48.0-24.bl.1.6, $\ldots$	$[ ]$	$1$
16731.c3	16731h4	16731.c	16731h	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{8} \cdot 11^{4} \cdot 13^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.11	2Cs	$3432$	$192$	$1$	$1$	$4$	$2$	$2$	$344064$	$2.372875$	$11779205551777/3763454409$	$0.95747$	$5.35513$	$[1, -1, 1, -720986, -157519384]$	\(y^2+xy+y=x^3-x^2-720986x-157519384\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.8, 12.24.0.c.1, 24.48.0-12.c.1.15, $\ldots$	$[ ]$	$1$
16731.c4	16731h2	16731.c	16731h	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{10} \cdot 11^{2} \cdot 13^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.14	2Cs	$3432$	$192$	$1$	$1$	$4$	$2$	$2$	$172032$	$2.026302$	$8732907467857/1656369$	$0.94339$	$5.32436$	$[1, -1, 1, -652541, -202693084]$	\(y^2+xy+y=x^3-x^2-652541x-202693084\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.10, 24.48.0-24.m.1.10, 88.48.0.?, $\ldots$	$[ ]$	$1$
16731.c5	16731h1	16731.c	16731h	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{14} \cdot 11 \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.8	2B	$6864$	$192$	$1$	$1$	$4$	$2$	$1$	$86016$	$1.679729$	$-1532808577/938223$	$0.88405$	$4.50933$	$[1, -1, 1, -36536, -3846670]$	\(y^2+xy+y=x^3-x^2-36536x-3846670\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.2, 24.24.0-8.n.1.8, $\ldots$	$[ ]$	$1$
16731.c6	16731h6	16731.c	16731h	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{7} \cdot 11^{2} \cdot 13^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.9	2B	$6864$	$192$	$1$	$1$	$4$	$2$	$0$	$688128$	$2.719452$	$266679605718863/296110251723$	$0.98475$	$5.67592$	$[1, -1, 1, 2039629, -1075147810]$	\(y^2+xy+y=x^3-x^2+2039629x-1075147810\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.12.0.n.1, 12.12.0.g.1, $\ldots$	$[ ]$	$1$
16731.d1	16731l2	16731.d	16731l	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{7} \cdot 11^{2} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1716$	$12$	$0$	$2.021869451$	$1$		$2$	$43008$	$1.460417$	$244140625/61347$	$1.08894$	$4.24623$	$[1, -1, 1, -19805, -801966]$	\(y^2+xy+y=x^3-x^2-19805x-801966\)	2.3.0.a.1, 12.6.0.a.1, 572.6.0.?, 1716.12.0.?	$[(218, 2172)]$	$1$
16731.d2	16731l1	16731.d	16731l	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{8} \cdot 11 \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1716$	$12$	$0$	$4.043738902$	$1$		$3$	$21504$	$1.113842$	$857375/1287$	$0.79548$	$3.71302$	$[1, -1, 1, 3010, -81012]$	\(y^2+xy+y=x^3-x^2+3010x-81012\)	2.3.0.a.1, 12.6.0.b.1, 286.6.0.?, 1716.12.0.?	$[(266, 4281)]$	$1$
16731.e1	16731a2	16731.e	16731a	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{9} \cdot 11^{2} \cdot 13^{12} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$4.914314866$	$1$		$2$	$483840$	$2.572510$	$23835655373139/584043889$	$0.96323$	$5.76651$	$[1, -1, 1, -2735804, 1705120876]$	\(y^2+xy+y=x^3-x^2-2735804x+1705120876\)	2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.?	$[(-1112, 58619)]$	$1$
16731.e2	16731a1	16731.e	16731a	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{9} \cdot 11^{4} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$9.828629732$	$1$		$1$	$241920$	$2.225937$	$17779581/32166277$	$1.02883$	$5.14323$	$[1, -1, 1, 24811, 84087748]$	\(y^2+xy+y=x^3-x^2+24811x+84087748\)	2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.?	$[(-57082/17, 42012058/17)]$	$1$
16731.f1	16731g1	16731.f	16731g	$1$	$1$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{13} \cdot 11^{2} \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$244608$	$2.337574$	$-2830523957248/264627$	$1.07225$	$5.73602$	$[0, 0, 1, -2478216, -1501730240]$	\(y^2+y=x^3-2478216x-1501730240\)	6.2.0.a.1	$[ ]$	$1$
16731.g1	16731j1	16731.g	16731j	$1$	$1$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{9} \cdot 11^{2} \cdot 13^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.611204160$	$1$		$4$	$10368$	$0.767960$	$5537792/3267$	$1.08782$	$3.32941$	$[0, 0, 1, 1014, 1732]$	\(y^2+y=x^3+1014x+1732\)	6.2.0.a.1	$[(16, 148)]$	$1$
16731.h1	16731e1	16731.h	16731e	$1$	$1$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{6} \cdot 11 \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$20160$	$1.142282$	$-262144/1859$	$0.89320$	$3.80897$	$[0, 0, 1, -2028, 127975]$	\(y^2+y=x^3-2028x+127975\)	22.2.0.a.1	$[ ]$	$1$
16731.i1	16731f1	16731.i	16731f	$1$	$1$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{9} \cdot 11^{2} \cdot 13^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$134784$	$2.050434$	$5537792/3267$	$1.08782$	$4.91190$	$[0, 0, 1, 171366, 3805753]$	\(y^2+y=x^3+171366x+3805753\)	6.2.0.a.1	$[ ]$	$1$
16731.j1	16731i1	16731.j	16731i	$1$	$1$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{13} \cdot 11^{2} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$3.038925034$	$1$		$2$	$18816$	$1.055098$	$-2830523957248/264627$	$1.07225$	$4.15354$	$[0, 0, 1, -14664, -683537]$	\(y^2+y=x^3-14664x-683537\)	6.2.0.a.1	$[(1351, 49450)]$	$1$
16731.k1	16731k3	16731.k	16731k	$4$	$4$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{9} \cdot 11^{4} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$2.108235297$	$1$		$4$	$110592$	$1.819149$	$347873904937/395307$	$1.00913$	$4.99294$	$[1, -1, 0, -222858, -40398539]$	\(y^2+xy=x^3-x^2-222858x-40398539\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 52.12.0-4.c.1.1, 88.12.0.?, $\ldots$	$[(-276, 307)]$	$1$
16731.k2	16731k2	16731.k	16731k	$4$	$4$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{12} \cdot 11^{2} \cdot 13^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1716$	$48$	$0$	$4.216470594$	$1$		$4$	$55296$	$1.472574$	$169112377/88209$	$1.00669$	$4.20847$	$[1, -1, 0, -17523, -276080]$	\(y^2+xy=x^3-x^2-17523x-276080\)	2.6.0.a.1, 12.12.0.a.1, 44.12.0.b.1, 52.12.0-2.a.1.1, 132.24.0.?, $\ldots$	$[(816, 22576)]$	$1$
16731.k3	16731k1	16731.k	16731k	$4$	$4$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{9} \cdot 11 \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$2.108235297$	$1$		$3$	$27648$	$1.126001$	$30664297/297$	$1.09706$	$4.03290$	$[1, -1, 0, -9918, 379471]$	\(y^2+xy=x^3-x^2-9918x+379471\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 52.12.0-4.c.1.2, 66.6.0.a.1, $\ldots$	$[(74, 179)]$	$1$
16731.k4	16731k4	16731.k	16731k	$4$	$4$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{18} \cdot 11 \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$8.432941188$	$1$		$0$	$110592$	$1.819149$	$9090072503/5845851$	$1.03763$	$4.61817$	$[1, -1, 0, 66132, -2200145]$	\(y^2+xy=x^3-x^2+66132x-2200145\)	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, $\ldots$	$[(50937/8, 11848487/8)]$	$1$
16731.l1	16731c2	16731.l	16731c	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{3} \cdot 11^{2} \cdot 13^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$0$	$161280$	$2.023205$	$23835655373139/584043889$	$0.96323$	$5.08870$	$[1, -1, 0, -303978, -63051299]$	\(y^2+xy=x^3-x^2-303978x-63051299\)	2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.?	$[ ]$	$1$
16731.l2	16731c1	16731.l	16731c	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{3} \cdot 11^{4} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$80640$	$1.676630$	$17779581/32166277$	$1.02883$	$4.46543$	$[1, -1, 0, 2757, -3115280]$	\(y^2+xy=x^3-x^2+2757x-3115280\)	2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.?	$[ ]$	$1$
16731.m1	16731d2	16731.m	16731d	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{3} \cdot 11^{2} \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$0$	$18432$	$0.793784$	$19034163/121$	$0.94120$	$3.64496$	$[1, -1, 0, -2820, 58033]$	\(y^2+xy=x^3-x^2-2820x+58033\)	2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.?	$[ ]$	$1$
16731.m2	16731d1	16731.m	16731d	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13^{2} \)	\( 3^{3} \cdot 11 \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$4$	$2$	$1$	$9216$	$0.447210$	$19683/11$	$1.13667$	$2.93810$	$[1, -1, 0, -285, -272]$	\(y^2+xy=x^3-x^2-285x-272\)	2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.?	$[ ]$	$1$

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