Elliptic curves over $\Q$ of conductor 152421

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

Results (22 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
152421.a1	152421a1	152421.a	152421a	$1$	$1$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{5} \cdot 23^{3} \cdot 47^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$138$	$2$	$0$	$0.411922925$	$1$		$18$	$126720$	$0.596482$	$13268119552/2956581$	$0.87751$	$2.59828$	$[0, 1, 1, -642, -5128]$	\(y^2+y=x^3+x^2-642x-5128\)	138.2.0.?	$[(33, 103), (-13, 34)]$	$1$
152421.b1	152421b1	152421.b	152421b	$1$	$1$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{5} \cdot 23^{3} \cdot 47^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$138$	$2$	$0$	$7.070180345$	$1$		$0$	$5955840$	$2.521557$	$13268119552/2956581$	$0.87751$	$4.53394$	$[0, 1, 1, -1418914, 509679604]$	\(y^2+y=x^3+x^2-1418914x+509679604\)	138.2.0.?	$[(3749/2, 15989/2)]$	$1$
152421.c1	152421e3	152421.c	152421e	$4$	$4$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{6} \cdot 23^{4} \cdot 47^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$8648$	$48$	$0$	$7.999286176$	$1$		$4$	$25012224$	$3.393913$	$674954705500996959793/9588192183$	$0.98392$	$5.95439$	$[1, 1, 1, -403688169, 3121718519400]$	\(y^2+xy+y=x^3+x^2-403688169x+3121718519400\)	2.3.0.a.1, 4.12.0-4.c.1.1, 184.24.0.?, 188.24.0.?, 8648.48.0.?	$[(-19041, 1985703)]$	$1$
152421.c2	152421e4	152421.c	152421e	$4$	$4$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{24} \cdot 23 \cdot 47^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$8648$	$48$	$0$	$31.99714470$	$1$		$0$	$25012224$	$3.393913$	$527860858731041233/305306328935961$	$1.09043$	$5.35498$	$[1, 1, 1, -37192979, -2067205984]$	\(y^2+xy+y=x^3+x^2-37192979x-2067205984\)	2.3.0.a.1, 4.12.0-4.c.1.2, 184.24.0.?, 376.24.0.?, 2162.6.0.?, $\ldots$	$[(-48779132316911/98112, 226503338558777005657/98112)]$	$1$
152421.c3	152421e2	152421.c	152421e	$4$	$4$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{12} \cdot 23^{2} \cdot 47^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$4324$	$48$	$0$	$15.99857235$	$1$		$2$	$12506112$	$3.047340$	$165231457514151553/621021226401$	$0.98614$	$5.25766$	$[1, 1, 1, -25253334, 48676285266]$	\(y^2+xy+y=x^3+x^2-25253334x+48676285266\)	2.6.0.a.1, 4.12.0-2.a.1.1, 92.24.0.?, 188.24.0.?, 4324.48.0.?	$[(-25372213/73, 97014514050/73)]$	$1$
152421.c4	152421e1	152421.c	152421e	$4$	$4$	\( 3 \cdot 23 \cdot 47^{2} \)	\( - 3^{6} \cdot 23 \cdot 47^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$8648$	$48$	$0$	$7.999286176$	$1$		$1$	$6253056$	$2.700768$	$-6411014266033/81817611327$	$0.93432$	$4.66950$	$[1, 1, 1, -854929, 1460491910]$	\(y^2+xy+y=x^3+x^2-854929x+1460491910\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 46.6.0.a.1, 92.12.0.?, $\ldots$	$[(408824/19, 298711503/19)]$	$1$
152421.d1	152421c2	152421.d	152421c	$2$	$2$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{2} \cdot 23^{4} \cdot 47^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.4	2B	$25944$	$48$	$1$	$2.335811913$	$1$		$6$	$156672$	$0.886082$	$5592359375/2518569$	$0.96770$	$2.84850$	$[1, 0, 0, -1738, 12989]$	\(y^2+xy=x^3-1738x+12989\)	2.3.0.a.1, 4.6.0.e.1, 24.12.0.bt.1, 184.12.0.?, 188.12.0.?, $\ldots$	$[(-4, 143), (-44, 91)]$	$1$
152421.d2	152421c1	152421.d	152421c	$2$	$2$	\( 3 \cdot 23 \cdot 47^{2} \)	\( - 3^{4} \cdot 23^{2} \cdot 47^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.4	2B	$25944$	$48$	$1$	$2.335811913$	$1$		$11$	$78336$	$0.539508$	$57066625/42849$	$0.85759$	$2.46432$	$[1, 0, 0, 377, 1568]$	\(y^2+xy=x^3+377x+1568\)	2.3.0.a.1, 4.6.0.e.1, 24.12.0.bq.1, 92.12.0.?, 94.6.0.?, $\ldots$	$[(-1, 35), (71, 587)]$	$1$
152421.e1	152421d2	152421.e	152421d	$2$	$2$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{2} \cdot 23^{4} \cdot 47^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.4	2B	$25944$	$48$	$1$	$15.28826786$	$1$		$0$	$7363584$	$2.811157$	$5592359375/2518569$	$0.96770$	$4.78415$	$[1, 0, 0, -3839288, -1363914039]$	\(y^2+xy=x^3-3839288x-1363914039\)	2.3.0.a.1, 4.6.0.e.1, 24.12.0.bt.1, 184.12.0.?, 188.12.0.?, $\ldots$	$[(6185848/37, 13622499523/37)]$	$1$
152421.e2	152421d1	152421.e	152421d	$2$	$2$	\( 3 \cdot 23 \cdot 47^{2} \)	\( - 3^{4} \cdot 23^{2} \cdot 47^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.4	2B	$25944$	$48$	$1$	$7.644133932$	$1$		$3$	$3681792$	$2.464581$	$57066625/42849$	$0.85759$	$4.39997$	$[1, 0, 0, 832747, -159463416]$	\(y^2+xy=x^3+832747x-159463416\)	2.3.0.a.1, 4.6.0.e.1, 24.12.0.bq.1, 92.12.0.?, 94.6.0.?, $\ldots$	$[(4291, 284956)]$	$1$
152421.f1	152421g1	152421.f	152421g	$1$	$1$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3 \cdot 23 \cdot 47^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$138$	$2$	$0$	$1.609854814$	$1$		$8$	$17664$	$-0.242973$	$1540096/69$	$0.73204$	$1.83902$	$[0, -1, 1, -31, 75]$	\(y^2+y=x^3-x^2-31x+75\)	138.2.0.?	$[(3, 0), (5, 4)]$	$1$
152421.g1	152421h1	152421.g	152421h	$1$	$1$	\( 3 \cdot 23 \cdot 47^{2} \)	\( - 3^{5} \cdot 23 \cdot 47^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6486$	$2$	$0$	$1$	$1$		$0$	$69120$	$0.367309$	$4096000/5589$	$0.84283$	$2.26923$	$[0, -1, 1, 157, 827]$	\(y^2+y=x^3-x^2+157x+827\)	6486.2.0.?	$[ ]$	$1$
152421.h1	152421i1	152421.h	152421i	$1$	$1$	\( 3 \cdot 23 \cdot 47^{2} \)	\( - 3^{5} \cdot 23 \cdot 47^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6486$	$2$	$0$	$23.44060738$	$1$		$0$	$3248640$	$2.292381$	$4096000/5589$	$0.84283$	$4.20488$	$[0, -1, 1, 346077, -91428649]$	\(y^2+y=x^3-x^2+346077x-91428649\)	6486.2.0.?	$[(4512122339639/34085, 9685231032580283512/34085)]$	$1$
152421.i1	152421j1	152421.i	152421j	$1$	$1$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3 \cdot 23 \cdot 47^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$138$	$2$	$0$	$12.77779544$	$1$		$0$	$830208$	$1.682100$	$1540096/69$	$0.73204$	$3.77468$	$[0, -1, 1, -69215, -6709081]$	\(y^2+y=x^3-x^2-69215x-6709081\)	138.2.0.?	$[(353661/2, 210317963/2)]$	$1$
152421.j1	152421f1	152421.j	152421f	$2$	$3$	\( 3 \cdot 23 \cdot 47^{2} \)	\( - 3^{3} \cdot 23 \cdot 47^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$6486$	$16$	$0$	$1$	$1$		$0$	$812544$	$1.893345$	$-1231925248000/29187$	$0.89592$	$4.26838$	$[0, 1, 1, -493343, -133541434]$	\(y^2+y=x^3+x^2-493343x-133541434\)	3.4.0.a.1, 138.8.0.?, 141.8.0.?, 6486.16.0.?	$[ ]$	$1$
152421.j2	152421f2	152421.j	152421f	$2$	$3$	\( 3 \cdot 23 \cdot 47^{2} \)	\( - 3 \cdot 23^{3} \cdot 47^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$6486$	$16$	$0$	$1$	$1$		$0$	$2437632$	$2.442650$	$-43614208000/3789643323$	$0.99585$	$4.40892$	$[0, 1, 1, -161993, -308580385]$	\(y^2+y=x^3+x^2-161993x-308580385\)	3.4.0.a.1, 138.8.0.?, 141.8.0.?, 6486.16.0.?	$[ ]$	$1$
152421.k1	152421l2	152421.k	152421l	$2$	$2$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{3} \cdot 23^{2} \cdot 47^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$12972$	$12$	$0$	$1$	$4$	$2$	$0$	$1695744$	$2.115688$	$510657175657/31551147$	$0.86444$	$4.19458$	$[1, 1, 0, -367844, 81003993]$	\(y^2+xy=x^3+x^2-367844x+81003993\)	2.3.0.a.1, 12.6.0.a.1, 4324.6.0.?, 12972.12.0.?	$[ ]$	$1$
152421.k2	152421l1	152421.k	152421l	$2$	$2$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{6} \cdot 23 \cdot 47^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$12972$	$12$	$0$	$1$	$4$	$2$	$1$	$847872$	$1.769115$	$3463512697/788049$	$0.81862$	$3.77618$	$[1, 1, 0, -69629, -5538000]$	\(y^2+xy=x^3+x^2-69629x-5538000\)	2.3.0.a.1, 12.6.0.b.1, 2162.6.0.?, 12972.12.0.?	$[ ]$	$1$
152421.l1	152421k2	152421.l	152421k	$2$	$2$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3 \cdot 23^{2} \cdot 47^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$0$	$423936$	$1.397680$	$413493625/1587$	$0.92463$	$3.59809$	$[1, 0, 1, -34286, 2432537]$	\(y^2+xy+y=x^3-34286x+2432537\)	2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.?	$[ ]$	$1$
152421.l2	152421k1	152421.l	152421k	$2$	$2$	\( 3 \cdot 23 \cdot 47^{2} \)	\( - 3^{2} \cdot 23 \cdot 47^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$211968$	$1.051107$	$-15625/207$	$0.99061$	$3.01071$	$[1, 0, 1, -1151, 73325]$	\(y^2+xy+y=x^3-1151x+73325\)	2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.?	$[ ]$	$1$
152421.m1	152421m1	152421.m	152421m	$1$	$1$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{3} \cdot 23 \cdot 47^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$138$	$2$	$0$	$1$	$4$	$2$	$0$	$126720$	$0.567578$	$9048064/621$	$0.80984$	$2.63261$	$[0, -1, 1, -736, -6975]$	\(y^2+y=x^3-x^2-736x-6975\)	138.2.0.?	$[ ]$	$1$
152421.n1	152421n1	152421.n	152421n	$1$	$1$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{3} \cdot 23 \cdot 47^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$138$	$2$	$0$	$58.49380365$	$1$		$0$	$5955840$	$2.492653$	$9048064/621$	$0.80984$	$4.56827$	$[0, -1, 1, -1626560, 750160589]$	\(y^2+y=x^3-x^2-1626560x+750160589\)	138.2.0.?	$[(26680974687019382503295517/174044804062, 1130402028079496086356858642870502429/174044804062)]$	$1$

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