Elliptic curves over $\Q$ of conductor 449352

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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
449352.a1	449352a1	449352.a	449352a	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( 2^{4} \cdot 3^{9} \cdot 79^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$948$	$12$	$0$	$8.274453733$	$1$		$1$	$22164480$	$2.543816$	$121485312/79$	$0.84503$	$4.41718$	$[0, 0, 0, -4381182, 3527694045]$	\(y^2=x^3-4381182x+3527694045\)	2.3.0.a.1, 12.6.0.c.1, 316.6.0.?, 474.6.0.?, 948.12.0.?	$[(53502/7, 2319057/7)]$	$1$
449352.a2	449352a2	449352.a	449352a	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{8} \cdot 3^{9} \cdot 79^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$948$	$12$	$0$	$4.137226866$	$1$		$3$	$44328960$	$2.890388$	$-4000752/6241$	$0.78340$	$4.46838$	$[0, 0, 0, -3538647, 4925459610]$	\(y^2=x^3-3538647x+4925459610\)	2.3.0.a.1, 6.6.0.a.1, 316.6.0.?, 948.12.0.?	$[(10981, 1135862)]$	$1$
449352.b1	449352b1	449352.b	449352b	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{8} \cdot 3^{9} \cdot 79^{2} \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1.026847398$	$1$		$36$	$569088$	$0.935077$	$-27747328/27$	$0.88927$	$2.92082$	$[0, 0, 0, -6636, 208244]$	\(y^2=x^3-6636x+208244\)	6.2.0.a.1	$[(46, 18), (49, 27), (22, 270)]$	$1$
449352.c1	449352c1	449352.c	449352c	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{8} \cdot 3^{9} \cdot 79^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$4$	$2$	$0$	$44957952$	$3.119801$	$-27747328/27$	$0.88927$	$4.93507$	$[0, 0, 0, -41415276, -102672413516]$	\(y^2=x^3-41415276x-102672413516\)	6.2.0.a.1	$[ ]$	$1$
449352.d1	449352d1	449352.d	449352d	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{10} \cdot 3^{11} \cdot 79^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$948$	$2$	$0$	$13.74763422$	$1$		$0$	$105164800$	$3.675842$	$-21437500/243$	$1.01472$	$5.35883$	$[0, 0, 0, -258845475, -1618531665874]$	\(y^2=x^3-258845475x-1618531665874\)	948.2.0.?	$[(5387324815/139, 394747437186756/139)]$	$1$
449352.e1	449352e1	449352.e	449352e	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{10} \cdot 3^{11} \cdot 79^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$948$	$2$	$0$	$2.269083991$	$1$		$2$	$1331200$	$1.491119$	$-21437500/243$	$1.01472$	$3.34458$	$[0, 0, 0, -41475, 3282766]$	\(y^2=x^3-41475x+3282766\)	948.2.0.?	$[(119, 180)]$	$1$
449352.f1	449352f1	449352.f	449352f	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( 2^{10} \cdot 3^{6} \cdot 79^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$316$	$2$	$0$	$0.686899503$	$9$	$3$	$4$	$11980800$	$2.396790$	$470596/79$	$1.06719$	$4.05680$	$[0, 0, 0, -917427, 284976542]$	\(y^2=x^3-917427x+284976542\)	316.2.0.?	$[(-553, 24964)]$	$1$
449352.g1	449352g1	449352.g	449352g	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( 2^{11} \cdot 3^{8} \cdot 79^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$38.45348699$	$1$		$0$	$34704384$	$3.002083$	$54194/9$	$0.78266$	$4.61541$	$[0, 0, 0, -10353819, 10828122518]$	\(y^2=x^3-10353819x+10828122518\)	8.2.0.b.1	$[(134396334737064046/6712253, 24355296695762785273364442/6712253)]$	$1$
449352.h1	449352h1	449352.h	449352h	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{10} \cdot 3^{7} \cdot 79^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$948$	$2$	$0$	$1$	$1$		$0$	$7987200$	$2.496571$	$-1556068/237$	$0.77069$	$4.16664$	$[0, 0, 0, -1366779, 691240678]$	\(y^2=x^3-1366779x+691240678\)	948.2.0.?	$[ ]$	$1$
449352.i1	449352i6	449352.i	449352i	$6$	$8$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( 2^{11} \cdot 3^{8} \cdot 79^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.210	2B	$3792$	$192$	$1$	$65.46413521$	$1$		$1$	$15814656$	$2.781826$	$3065617154/9$	$1.21059$	$4.78477$	$[0, 0, 0, -21587619, -38605939778]$	\(y^2=x^3-21587619x-38605939778\)	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, $\ldots$	$[(2112242872740073928357872599654/2558667426385, 3069520181625148780645606066287729506485643542/2558667426385)]$	$1$
449352.i2	449352i3	449352.i	449352i	$6$	$8$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( 2^{10} \cdot 3^{7} \cdot 79^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.127	2B	$3792$	$192$	$1$	$8.183016901$	$1$		$1$	$7907328$	$2.435253$	$28756228/3$	$1.05617$	$4.37278$	$[0, 0, 0, -3613539, 2643675118]$	\(y^2=x^3-3613539x+2643675118\)	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, $\ldots$	$[(184031/13, 108252/13)]$	$1$
449352.i3	449352i4	449352.i	449352i	$6$	$8$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( 2^{10} \cdot 3^{10} \cdot 79^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.88	2Cs	$1896$	$192$	$1$	$32.73206760$	$1$		$3$	$7907328$	$2.435253$	$1556068/81$	$1.03212$	$4.14869$	$[0, 0, 0, -1366779, -586716410]$	\(y^2=x^3-1366779x-586716410\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.e.2, 24.96.1.bl.2, 632.96.0.?, $\ldots$	$[(12944426360792046/200305, 1472723980790024610729094/200305)]$	$1$
449352.i4	449352i2	449352.i	449352i	$6$	$8$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( 2^{8} \cdot 3^{8} \cdot 79^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.138	2Cs	$1896$	$192$	$1$	$16.36603380$	$1$		$3$	$3953664$	$2.088676$	$35152/9$	$0.97255$	$3.75097$	$[0, 0, 0, -243399, 34512730]$	\(y^2=x^3-243399x+34512730\)	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, $\ldots$	$[(-89473453/403, 77402659320/403)]$	$1$
449352.i5	449352i1	449352.i	449352i	$6$	$8$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{4} \cdot 3^{7} \cdot 79^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.150	2B	$3792$	$192$	$1$	$8.183016901$	$1$		$1$	$1976832$	$1.742104$	$2048/3$	$1.17572$	$3.35227$	$[0, 0, 0, 37446, 3451273]$	\(y^2=x^3+37446x+3451273\)	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, $\ldots$	$[(178224/35, 148392257/35)]$	$1$
449352.i6	449352i5	449352.i	449352i	$6$	$8$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{11} \cdot 3^{14} \cdot 79^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.218	2B	$3792$	$192$	$1$	$65.46413521$	$1$		$1$	$15814656$	$2.781826$	$207646/6561$	$1.15980$	$4.35311$	$[0, 0, 0, 879981, -2326158002]$	\(y^2=x^3+879981x-2326158002\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0.m.1, 48.96.1.w.2, 948.12.0.?, $\ldots$	$[(2124615887806550544585234949254/2566206105365, 3096866313301053320891229707938010163469737758/2566206105365)]$	$1$
449352.j1	449352j1	449352.j	449352j	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{10} \cdot 3^{19} \cdot 79^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$948$	$2$	$0$	$118.0396007$	$1$		$0$	$560701440$	$4.297447$	$-1402386001982788/786063417597$	$0.99300$	$5.78493$	$[0, 0, 0, -1320214899, -25905451367522]$	\(y^2=x^3-1320214899x-25905451367522\)	948.2.0.?	$[(10371217220133712911014936039691272558068613373177119/478867897271023458164089, 288376243157312705987953628347338761683220526995685017575809221869962252434436/478867897271023458164089)]$	$1$
449352.k1	449352k1	449352.k	449352k	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( 2^{11} \cdot 3^{8} \cdot 79^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$1$	$4$	$2$	$0$	$439296$	$0.817359$	$54194/9$	$0.78266$	$2.60116$	$[0, 0, 0, -1659, -21962]$	\(y^2=x^3-1659x-21962\)	8.2.0.b.1	$[ ]$	$1$
449352.l1	449352l1	449352.l	449352l	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( 2^{4} \cdot 3^{3} \cdot 79^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$948$	$12$	$0$	$1$	$9$	$3$	$1$	$7388160$	$1.994507$	$121485312/79$	$0.84503$	$3.91074$	$[0, 0, 0, -486798, -130655335]$	\(y^2=x^3-486798x-130655335\)	2.3.0.a.1, 12.6.0.c.1, 316.6.0.?, 474.6.0.?, 948.12.0.?	$[ ]$	$1$
449352.l2	449352l2	449352.l	449352l	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 79^{2} \)	\( - 2^{8} \cdot 3^{3} \cdot 79^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$948$	$12$	$0$	$1$	$9$	$3$	$1$	$14776320$	$2.341080$	$-4000752/6241$	$0.78340$	$3.96194$	$[0, 0, 0, -393183, -182424430]$	\(y^2=x^3-393183x-182424430\)	2.3.0.a.1, 6.6.0.a.1, 316.6.0.?, 948.12.0.?	$[ ]$	$1$

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