Elliptic curves over $\Q$ of conductor 479408

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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
479408.a1	479408a1	479408.a	479408a	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{8} \cdot 19^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.356327878$	$1$		$2$	$2211840$	$1.005833$	$-148176/83$	$0.66708$	$2.73655$	$[0, 0, 0, -2527, 68590]$	\(y^2=x^3-2527x+68590\)	166.2.0.?	$[(133, 1444)]$
479408.b1	479408b1	479408.b	479408b	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( 2^{4} \cdot 19^{2} \cdot 83^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$6308$	$12$	$0$	$4.850493384$	$1$		$2$	$188928$	$0.243169$	$288527616/6889$	$0.74861$	$2.15146$	$[0, 0, 0, -247, -1463]$	\(y^2=x^3-247x-1463\)	2.2.0.a.1, 38.6.0.a.1, 6308.12.0.?	$[(-8, 1), (73/2, 83/2)]$
479408.c1	479408c1	479408.c	479408c	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{25} \cdot 19^{2} \cdot 83 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$664$	$2$	$0$	$2.252584788$	$1$		$10$	$696384$	$1.161875$	$-177724461817/679936$	$0.93144$	$3.06696$	$[0, 1, 0, -13344, 590836]$	\(y^2=x^3+x^2-13344x+590836\)	664.2.0.?	$[(26, 512), (1674/5, 5632/5)]$
479408.d1	479408d1	479408.d	479408d	$2$	$2$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( 2^{12} \cdot 19^{3} \cdot 83 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6308$	$12$	$0$	$2.793793038$	$1$		$13$	$259840$	$0.504973$	$300763/83$	$0.70586$	$2.27557$	$[0, 1, 0, -424, 2292]$	\(y^2=x^3+x^2-424x+2292\)	2.3.0.a.1, 76.6.0.?, 332.6.0.?, 3154.6.0.?, 6308.12.0.?	$[(-2, 56), (22, 64)]$
479408.d2	479408d2	479408.d	479408d	$2$	$2$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{12} \cdot 19^{3} \cdot 83^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6308$	$12$	$0$	$2.793793038$	$1$		$13$	$519680$	$0.851547$	$5177717/6889$	$0.78719$	$2.51314$	$[0, 1, 0, 1096, 16276]$	\(y^2=x^3+x^2+1096x+16276\)	2.3.0.a.1, 38.6.0.b.1, 332.6.0.?, 6308.12.0.?	$[(6, 152), (734, 19920)]$
479408.e1	479408e1	479408.e	479408e	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{8} \cdot 19^{9} \cdot 83^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1$	$1$		$0$	$9538560$	$2.244453$	$-7465061395456/47251651$	$0.86501$	$4.04149$	$[0, 1, 0, -933305, 348625027]$	\(y^2=x^3+x^2-933305x+348625027\)	38.2.0.a.1	$[ ]$
479408.f1	479408f1	479408.f	479408f	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{8} \cdot 19^{7} \cdot 83^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$2.351752958$	$1$		$10$	$1589760$	$1.604492$	$179830784/130891$	$0.84483$	$3.22770$	$[0, 1, 0, 26955, 873727]$	\(y^2=x^3+x^2+26955x+873727\)	38.2.0.a.1	$[(-13, 722), (747, 20938)]$
479408.g1	479408g1	479408.g	479408g	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{8} \cdot 19^{7} \cdot 83^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$7.716212742$	$1$		$0$	$5391360$	$2.164948$	$-62345200132096/130891$	$0.90384$	$4.20292$	$[0, 1, 0, -1893565, -1003558233]$	\(y^2=x^3+x^2-1893565x-1003558233\)	38.2.0.a.1	$[(547319/17, 230775026/17)]$
479408.h1	479408h1	479408.h	479408h	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{13} \cdot 19^{8} \cdot 83^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$664$	$2$	$0$	$1$	$4$	$2$	$0$	$15266880$	$2.503216$	$605245247/1143574$	$0.89844$	$4.04516$	$[0, 1, 0, 724768, -357175820]$	\(y^2=x^3+x^2+724768x-357175820\)	664.2.0.?	$[ ]$
479408.i1	479408i1	479408.i	479408i	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{8} \cdot 19^{7} \cdot 83^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$10.25020489$	$1$		$0$	$11335680$	$2.341927$	$-444209247232/901708099$	$0.86719$	$3.94006$	$[0, 1, 0, -364369, -179858757]$	\(y^2=x^3+x^2-364369x-179858757\)	38.2.0.a.1	$[(11637694/87, 35443801997/87)]$
479408.j1	479408j1	479408.j	479408j	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( 2^{4} \cdot 19^{8} \cdot 83^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$6308$	$12$	$0$	$2.498997301$	$1$		$0$	$3633408$	$1.904171$	$21064753408/6889$	$0.81531$	$3.83011$	$[0, -1, 0, -372672, -87417701]$	\(y^2=x^3-x^2-372672x-87417701\)	2.2.0.a.1, 38.6.0.a.1, 332.4.0.?, 6308.12.0.?	$[(4213/2, 209741/2)]$
479408.k1	479408k1	479408.k	479408k	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{16} \cdot 19^{6} \cdot 83 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$2.665143943$	$1$		$8$	$1368576$	$1.530304$	$-30664297/1328$	$0.83983$	$3.30995$	$[0, -1, 0, -37664, 2929408]$	\(y^2=x^3-x^2-37664x+2929408\)	166.2.0.?	$[(146, 722), (592/3, 23104/3)]$
479408.l1	479408l1	479408.l	479408l	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{12} \cdot 19^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$912384$	$1.221498$	$103823/83$	$0.77332$	$2.86957$	$[0, -1, 0, 5656, -102992]$	\(y^2=x^3-x^2+5656x-102992\)	166.2.0.?	$[ ]$
479408.m1	479408m1	479408.m	479408m	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{10} \cdot 19^{12} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$18109440$	$2.870655$	$-13636809560150500/3904808123$	$0.91802$	$4.72085$	$[0, -1, 0, -18110768, -29666921264]$	\(y^2=x^3-x^2-18110768x-29666921264\)	166.2.0.?	$[ ]$
479408.n1	479408n1	479408.n	479408n	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{22} \cdot 19^{8} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$3.671777739$	$1$		$0$	$10368000$	$2.690044$	$-842971295994625/30682112$	$0.90933$	$4.61399$	$[0, -1, 0, -11367288, 14755659376]$	\(y^2=x^3-x^2-11367288x+14755659376\)	166.2.0.?	$[(26812/3, 2310400/3)]$
479408.o1	479408o1	479408.o	479408o	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{4} \cdot 19^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$221184$	$0.784133$	$-256000/83$	$0.71692$	$2.54864$	$[0, -1, 0, -1203, 20470]$	\(y^2=x^3-x^2-1203x+20470\)	166.2.0.?	$[ ]$
479408.p1	479408p1	479408.p	479408p	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{4} \cdot 19^{8} \cdot 83^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$20839680$	$2.819187$	$-8605300751925035008/206415107$	$0.98175$	$4.89577$	$[0, -1, 0, -38835417, 93164495488]$	\(y^2=x^3-x^2-38835417x+93164495488\)	166.2.0.?	$[ ]$
479408.q1	479408q3	479408.q	479408q	$4$	$4$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( 2^{14} \cdot 19^{10} \cdot 83 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$12616$	$48$	$0$	$1$	$1$		$1$	$11059200$	$2.683968$	$621808094281977/43266572$	$0.98612$	$4.59072$	$[0, 0, 0, -10270811, 12668614154]$	\(y^2=x^3-10270811x+12668614154\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 76.12.0.?, 152.24.0.?, $\ldots$	$[ ]$
479408.q2	479408q2	479408.q	479408q	$4$	$4$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( 2^{16} \cdot 19^{8} \cdot 83^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$6308$	$48$	$0$	$1$	$1$		$3$	$5529600$	$2.337391$	$182573756217/39790864$	$0.98034$	$3.96893$	$[0, 0, 0, -682651, 171406410]$	\(y^2=x^3-682651x+171406410\)	2.6.0.a.1, 4.12.0-2.a.1.1, 76.24.0.?, 332.24.0.?, 6308.48.0.?	$[ ]$
479408.q3	479408q1	479408.q	479408q	$4$	$4$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( 2^{20} \cdot 19^{7} \cdot 83 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$12616$	$48$	$0$	$1$	$1$		$1$	$2764800$	$1.990820$	$6158676537/403712$	$0.81948$	$3.70982$	$[0, 0, 0, -220571, -37546166]$	\(y^2=x^3-220571x-37546166\)	2.3.0.a.1, 4.12.0-4.c.1.2, 152.24.0.?, 664.24.0.?, 3154.6.0.?, $\ldots$	$[ ]$
479408.q4	479408q4	479408.q	479408q	$4$	$4$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{14} \cdot 19^{7} \cdot 83^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$12616$	$48$	$0$	$1$	$1$		$3$	$11059200$	$2.683968$	$1984699888263/3606832396$	$0.94665$	$4.20952$	$[0, 0, 0, 1512229, 1047163530]$	\(y^2=x^3+1512229x+1047163530\)	2.3.0.a.1, 4.12.0-4.c.1.1, 38.6.0.b.1, 76.24.0.?, 664.24.0.?, $\ldots$	$[ ]$
479408.r1	479408r1	479408.r	479408r	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( 2^{4} \cdot 19^{2} \cdot 83^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$6308$	$12$	$0$	$3.303547785$	$1$		$4$	$191232$	$0.431952$	$21064753408/6889$	$0.81531$	$2.47948$	$[0, 1, 0, -1032, 12419]$	\(y^2=x^3+x^2-1032x+12419\)	2.2.0.a.1, 38.6.0.a.1, 6308.12.0.?	$[(-35, 83), (109/2, 581/2)]$
479408.s1	479408s1	479408.s	479408s	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{4} \cdot 19^{8} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.859347883$	$1$		$2$	$725760$	$1.246399$	$-5619712/29963$	$0.76342$	$2.92843$	$[0, 1, 0, -3369, 239450]$	\(y^2=x^3+x^2-3369x+239450\)	166.2.0.?	$[(82, 722)]$
479408.t1	479408t1	479408.t	479408t	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{4} \cdot 19^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$228096$	$0.751348$	$2048/83$	$0.76681$	$2.46924$	$[0, 1, 0, 241, 12020]$	\(y^2=x^3+x^2+241x+12020\)	166.2.0.?	$[ ]$
479408.u1	479408u1	479408.u	479408u	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{8} \cdot 19^{10} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$4.501065227$	$1$		$0$	$3594240$	$1.969269$	$6885902000/10816643$	$0.80329$	$3.54759$	$[0, 1, 0, 90852, 13831100]$	\(y^2=x^3+x^2+90852x+13831100\)	166.2.0.?	$[(-782/3, 62092/3)]$
479408.v1	479408v1	479408.v	479408v	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{29} \cdot 19^{7} \cdot 83^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$152$	$2$	$0$	$2.888615576$	$1$		$0$	$31726080$	$2.909565$	$-611722215487369/17156145152$	$0.90794$	$4.59309$	$[0, 1, 0, -10214976, 12863695412]$	\(y^2=x^3+x^2-10214976x+12863695412\)	152.2.0.?	$[(6997/2, 149815/2)]$
479408.w1	479408w1	479408.w	479408w	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{8} \cdot 19^{13} \cdot 83^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$18.02969424$	$1$		$0$	$42094080$	$3.074493$	$5014948370604032/6157882409971$	$0.95589$	$4.54714$	$[0, -1, 0, 8174003, 9524402961]$	\(y^2=x^3-x^2+8174003x+9524402961\)	38.2.0.a.1	$[(20918438169/1201, 3088236723615546/1201)]$
479408.x1	479408x1	479408.x	479408x	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{25} \cdot 19^{8} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$664$	$2$	$0$	$53.61178986$	$1$		$0$	$13231296$	$2.634094$	$-177724461817/679936$	$0.93144$	$4.41758$	$[0, -1, 0, -4817304, -4081447696]$	\(y^2=x^3-x^2-4817304x-4081447696\)	664.2.0.?	$[(145326965560341928925645/6067751777, 43770221724206989200785796761023674/6067751777)]$
479408.y1	479408y1	479408.y	479408y	$2$	$2$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( 2^{12} \cdot 19^{9} \cdot 83 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6308$	$12$	$0$	$1$	$9$	$3$	$1$	$4936960$	$1.977194$	$300763/83$	$0.70586$	$3.62620$	$[0, -1, 0, -153184, -16639680]$	\(y^2=x^3-x^2-153184x-16639680\)	2.3.0.a.1, 76.6.0.?, 332.6.0.?, 3154.6.0.?, 6308.12.0.?	$[ ]$
479408.y2	479408y2	479408.y	479408y	$2$	$2$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{12} \cdot 19^{9} \cdot 83^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6308$	$12$	$0$	$1$	$9$	$3$	$1$	$9873920$	$2.323765$	$5177717/6889$	$0.78719$	$3.86377$	$[0, -1, 0, 395536, -109263616]$	\(y^2=x^3-x^2+395536x-109263616\)	2.3.0.a.1, 38.6.0.b.1, 332.6.0.?, 6308.12.0.?	$[ ]$
479408.z1	479408z1	479408.z	479408z	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{12} \cdot 19^{9} \cdot 83^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1$	$1$		$0$	$10368000$	$2.318504$	$2887553024/47251651$	$0.86967$	$3.90466$	$[0, -1, 0, 171355, -142647091]$	\(y^2=x^3-x^2+171355x-142647091\)	38.2.0.a.1	$[ ]$
479408.ba1	479408ba1	479408.ba	479408ba	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{13} \cdot 19^{2} \cdot 83^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$664$	$2$	$0$	$16.52102804$	$1$		$0$	$803520$	$1.030996$	$605245247/1143574$	$0.89844$	$2.69453$	$[0, -1, 0, 2008, 51440]$	\(y^2=x^3-x^2+2008x+51440\)	664.2.0.?	$[(14031409/184, 52821734775/184)]$
479408.bb1	479408bb1	479408.bb	479408bb	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{14} \cdot 19^{8} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$9.555383103$	$1$		$0$	$4561920$	$1.818762$	$3375/119852$	$0.93017$	$3.45046$	$[0, 0, 0, 1805, -7311694]$	\(y^2=x^3+1805x-7311694\)	166.2.0.?	$[(1325497/39, 1519417232/39)]$
479408.bc1	479408bc1	479408.bc	479408bc	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( 2^{4} \cdot 19^{8} \cdot 83^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$6308$	$12$	$0$	$5.668181976$	$1$		$0$	$3589632$	$1.715389$	$288527616/6889$	$0.74861$	$3.50209$	$[0, 0, 0, -89167, 10034717]$	\(y^2=x^3-89167x+10034717\)	2.2.0.a.1, 38.6.0.a.1, 332.4.0.?, 6308.12.0.?	$[(173641/30, 3086189/30)]$
479408.bd1	479408bd1	479408.bd	479408bd	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{10} \cdot 19^{8} \cdot 83^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$36$	$2, 3$	$0$	$108979200$	$3.070152$	$1977478112299644/1421993672123$	$0.95373$	$4.57319$	$[0, 0, 0, 9514877, -5564089390]$	\(y^2=x^3+9514877x-5564089390\)	166.2.0.?	$[ ]$

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