Elliptic curves over $\Q$ of conductor 8664

Results (26 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
8664.a1	8664k1	8664.a	8664k	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{6} \cdot 19^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1.423529556$	$1$		$4$	$34560$	$1.455542$	$-81415168/13851$	$0.91437$	$4.59743$	$[0, -1, 0, -20697, -1296819]$	\(y^2=x^3-x^2-20697x-1296819\)	38.2.0.a.1	$[(735, 19494)]$
8664.b1	8664b1	8664.b	8664b	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{5} \cdot 19^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.5.0.1	5S4	$30$	$10$	$0$	$1.871605023$	$1$		$2$	$54720$	$1.571154$	$-104272/243$	$0.87512$	$4.66203$	$[0, -1, 0, -16004, -1741932]$	\(y^2=x^3-x^2-16004x-1741932\)	5.5.0.a.1, 6.2.0.a.1, 30.10.0.a.1	$[(241, 2888)]$
8664.c1	8664a2	8664.c	8664a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$0.644170958$	$1$		$7$	$3200$	$0.327095$	$1203052/9$	$1.19561$	$3.28283$	$[0, -1, 0, -424, 3484]$	\(y^2=x^3-x^2-424x+3484\)	2.3.0.a.1, 12.6.0.g.1, 76.6.0.?, 228.12.0.?	$[(-6, 76)]$
8664.c2	8664a1	8664.c	8664a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{8} \cdot 3 \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1.288341917$	$1$		$5$	$1600$	$-0.019479$	$5488/3$	$0.87364$	$2.53546$	$[0, -1, 0, -44, -12]$	\(y^2=x^3-x^2-44x-12\)	2.3.0.a.1, 12.6.0.g.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[(-2, 8)]$
8664.d1	8664h1	8664.d	8664h	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{3} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.645325887$	$1$		$4$	$864$	$-0.160540$	$-4864000/27$	$0.93971$	$2.65452$	$[0, -1, 0, -63, 216]$	\(y^2=x^3-x^2-63x+216\)	6.2.0.a.1	$[(5, 1)]$
8664.e1	8664j1	8664.e	8664j	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{3} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.974775547$	$1$		$4$	$864$	$-0.314999$	$38912/27$	$0.92397$	$2.12095$	$[0, -1, 0, 13, -12]$	\(y^2=x^3-x^2+13x-12\)	6.2.0.a.1	$[(1, 1)]$
8664.f1	8664i3	8664.f	8664i	$4$	$4$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{11} \cdot 3^{3} \cdot 19^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$456$	$48$	$0$	$22.84477309$	$1$		$1$	$69120$	$2.138420$	$111223479026/3518667$	$0.97692$	$5.59462$	$[0, -1, 0, -459312, -116340660]$	\(y^2=x^3-x^2-459312x-116340660\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 24.24.0-24.s.1.6, 152.24.0.?, $\ldots$	$[(-10040833307/4818, 123419370439925/4818)]$
8664.f2	8664i2	8664.f	8664i	$4$	$4$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{6} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$456$	$48$	$0$	$11.42238654$	$1$		$3$	$34560$	$1.791849$	$768400132/263169$	$0.94504$	$4.96948$	$[0, -1, 0, -69432, 4522140]$	\(y^2=x^3-x^2-69432x+4522140\)	2.6.0.a.1, 4.12.0-2.a.1.1, 24.24.0-24.b.1.6, 152.24.0.?, 228.24.0.?, $\ldots$	$[(71230/33, 18191600/33)]$
8664.f3	8664i1	8664.f	8664i	$4$	$4$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{3} \cdot 19^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$456$	$48$	$0$	$5.711193274$	$1$		$5$	$17280$	$1.445274$	$2211014608/513$	$0.92081$	$4.93315$	$[0, -1, 0, -62212, 5992132]$	\(y^2=x^3-x^2-62212x+5992132\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.y.1.13, 114.6.0.?, 152.24.0.?, $\ldots$	$[(12021, 1317650)]$
8664.f4	8664i4	8664.f	8664i	$4$	$4$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{11} \cdot 3^{12} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$456$	$48$	$0$	$22.84477309$	$1$		$1$	$69120$	$2.138420$	$9878111854/10097379$	$0.98646$	$5.32758$	$[0, -1, 0, 204928, 31189932]$	\(y^2=x^3-x^2+204928x+31189932\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.y.1.5, 152.24.0.?, 456.48.0.?	$[(8178750889/825, 740157730649162/825)]$
8664.g1	8664c1	8664.g	8664c	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{16} \cdot 19^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.4.0.1		$76$	$8$	$0$	$4.634729436$	$1$		$2$	$486400$	$2.817566$	$-4434684928/43046721$	$1.11199$	$6.30153$	$[0, -1, 0, -1490689, -2952847259]$	\(y^2=x^3-x^2-1490689x-2952847259\)	4.4.0.a.1, 38.2.0.a.1, 76.8.0.?	$[(18865, 2585034)]$
8664.h1	8664n1	8664.h	8664n	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{5} \cdot 19^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.5.0.1	5S4	$30$	$10$	$0$	$0.143659457$	$1$		$24$	$2880$	$0.098933$	$-104272/243$	$0.87512$	$2.71356$	$[0, 1, 0, -44, 240]$	\(y^2=x^3+x^2-44x+240\)	5.5.0.a.1, 6.2.0.a.1, 30.10.0.a.1	$[(-2, 18), (10, 30)]$
8664.i1	8664l2	8664.i	8664l	$2$	$2$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$8.298811729$	$1$		$1$	$60800$	$1.799314$	$1203052/9$	$1.19561$	$5.23129$	$[0, 1, 0, -153184, -22977904]$	\(y^2=x^3+x^2-153184x-22977904\)	2.3.0.a.1, 12.6.0.g.1, 76.6.0.?, 228.12.0.?	$[(-17120/9, 29204/9)]$
8664.i2	8664l1	8664.i	8664l	$2$	$2$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{8} \cdot 3 \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$4.149405864$	$1$		$3$	$30400$	$1.452740$	$5488/3$	$0.87364$	$4.48393$	$[0, 1, 0, -16004, 178080]$	\(y^2=x^3+x^2-16004x+178080\)	2.3.0.a.1, 12.6.0.g.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[(-42, 882)]$
8664.j1	8664g5	8664.j	8664g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{11} \cdot 3^{2} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.210	2B	$912$	$192$	$1$	$6.250380335$	$1$		$3$	$27648$	$1.520014$	$3065617154/9$	$1.21059$	$5.19854$	$[0, 1, 0, -138744, 19845360]$	\(y^2=x^3+x^2-138744x+19845360\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.r.1, 16.48.0.l.1, 24.48.0.bf.1, $\ldots$	$[(999, 29652)]$
8664.j2	8664g3	8664.j	8664g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{10} \cdot 3 \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.127	2B	$912$	$192$	$1$	$12.50076067$	$1$		$1$	$13824$	$1.173441$	$28756228/3$	$1.05617$	$4.60712$	$[0, 1, 0, -23224, -1369888]$	\(y^2=x^3+x^2-23224x-1369888\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0.h.1, 16.48.0.bb.2, $\ldots$	$[(-1245929/119, 16258920/119)]$
8664.j3	8664g4	8664.j	8664g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{4} \cdot 19^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.88	2Cs	$456$	$192$	$1$	$3.125190167$	$1$		$7$	$13824$	$1.173441$	$1556068/81$	$1.03212$	$4.28544$	$[0, 1, 0, -8784, 299376]$	\(y^2=x^3+x^2-8784x+299376\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.e.2, 24.96.1.bl.2, 76.24.0.?, $\ldots$	$[(-84, 672)]$
8664.j4	8664g2	8664.j	8664g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{2} \cdot 19^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.138	2Cs	$456$	$192$	$1$	$6.250380335$	$1$		$3$	$6912$	$0.826867$	$35152/9$	$0.97255$	$3.71451$	$[0, 1, 0, -1564, -18304]$	\(y^2=x^3+x^2-1564x-18304\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.h.1, 12.24.0.c.1, 24.96.1.bu.1, $\ldots$	$[(-1312/7, 24480/7)]$
8664.j5	8664g1	8664.j	8664g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{4} \cdot 3 \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.150	2B	$912$	$192$	$1$	$3.125190167$	$1$		$1$	$3456$	$0.480294$	$2048/3$	$1.17572$	$3.14218$	$[0, 1, 0, 241, -1698]$	\(y^2=x^3+x^2+241x-1698\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.ba.1, 12.12.0.g.1, $\ldots$	$[(529/3, 12635/3)]$
8664.j6	8664g6	8664.j	8664g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{11} \cdot 3^{8} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.218	2B	$912$	$192$	$1$	$1.562595083$	$1$		$3$	$27648$	$1.520014$	$207646/6561$	$1.15980$	$4.57888$	$[0, 1, 0, 5656, 1200432]$	\(y^2=x^3+x^2+5656x+1200432\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0.m.1, 48.96.1.w.2, 76.12.0.?, $\ldots$	$[(139, 2166)]$
8664.k1	8664d1	8664.k	8664d	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{3} \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$16416$	$1.311680$	$-4864000/27$	$0.93971$	$4.60299$	$[0, 1, 0, -22863, -1344618]$	\(y^2=x^3+x^2-22863x-1344618\)	6.2.0.a.1	$[]$
8664.l1	8664f1	8664.l	8664f	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{2} \cdot 19^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1.095502006$	$1$		$4$	$34560$	$1.541025$	$70575104/61731$	$0.95058$	$4.55325$	$[0, 1, 0, 19735, -756549]$	\(y^2=x^3+x^2+19735x-756549\)	38.2.0.a.1	$[(139, 2166)]$
8664.m1	8664e1	8664.m	8664e	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{3} \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$16416$	$1.157221$	$38912/27$	$0.92397$	$4.06942$	$[0, 1, 0, 4573, 54618]$	\(y^2=x^3+x^2+4573x+54618\)	6.2.0.a.1	$[]$
8664.n1	8664m1	8664.n	8664m	$1$	$1$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{16} \cdot 19^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.4.0.1		$76$	$8$	$0$	$0.183900085$	$1$		$6$	$25600$	$1.345346$	$-4434684928/43046721$	$1.11199$	$4.35306$	$[0, 1, 0, -4129, 429203]$	\(y^2=x^3+x^2-4129x+429203\)	4.4.0.a.1, 38.2.0.a.1, 76.8.0.?	$[(101, 1026)]$
8664.o1	8664o1	8664.o	8664o	$2$	$2$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( 2^{10} \cdot 3 \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$456$	$12$	$0$	$1$	$9$	$3$	$1$	$28800$	$1.117296$	$470596/57$	$0.94139$	$4.15354$	$[0, 1, 0, -5896, -156928]$	\(y^2=x^3+x^2-5896x-156928\)	2.3.0.a.1, 8.6.0.d.1, 114.6.0.?, 456.12.0.?	$[]$
8664.o2	8664o2	8664.o	8664o	$2$	$2$	\( 2^{3} \cdot 3 \cdot 19^{2} \)	\( - 2^{11} \cdot 3^{2} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$456$	$12$	$0$	$1$	$9$	$3$	$1$	$57600$	$1.463869$	$715822/3249$	$0.90786$	$4.48836$	$[0, 1, 0, 8544, -792288]$	\(y^2=x^3+x^2+8544x-792288\)	2.3.0.a.1, 8.6.0.a.1, 228.6.0.?, 456.12.0.?	$[]$