Elliptic curves over $\Q$ of conductor 227154

Results (32 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
227154.a1	227154t1	227154.a	227154t	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{11} \cdot 3 \cdot 17^{6} \cdot 131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3144$	$2$	$0$	$15.58766358$	$1$		$0$	$1262976$	$1.384295$	$119168121961/804864$	$0.91365$	$3.44618$	$[1, 1, 0, -29628, -1963824]$	\(y^2+xy=x^3+x^2-29628x-1963824\)	3144.2.0.?	$[(-9958141/310, 4047678207/310)]$
227154.b1	227154u1	227154.b	227154u	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{13} \cdot 3^{4} \cdot 17^{10} \cdot 131 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1048$	$2$	$0$	$1$	$1$		$0$	$6709248$	$2.590965$	$-15962082856161625/7260088983552$	$0.92681$	$4.45038$	$[1, 1, 0, -1515955, -960723347]$	\(y^2+xy=x^3+x^2-1515955x-960723347\)	1048.2.0.?	$[ ]$
227154.c1	227154v1	227154.c	227154v	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{2} \cdot 3^{7} \cdot 17^{6} \cdot 131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1572$	$2$	$0$	$4.450920004$	$1$		$2$	$739200$	$1.267689$	$-498677257/1145988$	$0.89539$	$3.13218$	$[1, 1, 0, -4774, 281128]$	\(y^2+xy=x^3+x^2-4774x+281128\)	1572.2.0.?	$[(84, 652)]$
227154.d1	227154w2	227154.d	227154w	$2$	$3$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{3} \cdot 3 \cdot 17^{6} \cdot 131^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$53448$	$16$	$0$	$1$	$1$		$0$	$2298240$	$1.622341$	$333822098953/53954184$	$0.92728$	$3.52970$	$[1, 1, 0, -41766, -2806548]$	\(y^2+xy=x^3+x^2-41766x-2806548\)	3.4.0.a.1, 51.8.0-3.a.1.1, 3144.8.0.?, 53448.16.0.?	$[ ]$
227154.d2	227154w1	227154.d	227154w	$2$	$3$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2 \cdot 3^{3} \cdot 17^{6} \cdot 131 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$53448$	$16$	$0$	$1$	$1$		$0$	$766080$	$1.073036$	$6826561273/7074$	$0.88675$	$3.21431$	$[1, 1, 0, -11421, 464643]$	\(y^2+xy=x^3+x^2-11421x+464643\)	3.4.0.a.1, 51.8.0-3.a.1.2, 3144.8.0.?, 53448.16.0.?	$[ ]$
227154.e1	227154n1	227154.e	227154n	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{9} \cdot 3^{24} \cdot 17^{6} \cdot 131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1048$	$2$	$0$	$1.361825775$	$1$		$2$	$66355200$	$3.218845$	$199084633070471/18943113870853632$	$1.16714$	$5.02167$	$[1, 0, 1, 351562, 32533414472]$	\(y^2+xy+y=x^3+351562x+32533414472\)	1048.2.0.?	$[(-1098, 176116)]$
227154.f1	227154o1	227154.f	227154o	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{10} \cdot 3^{4} \cdot 17^{9} \cdot 131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$4454$	$2$	$0$	$0.702074827$	$1$		$4$	$3870720$	$2.154877$	$-946098541513/53383007232$	$0.92497$	$3.98633$	$[1, 0, 1, -59107, 54888734]$	\(y^2+xy+y=x^3-59107x+54888734\)	4454.2.0.?	$[(-248, 7493)]$
227154.g1	227154p3	227154.g	227154p	$4$	$4$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{3} \cdot 3^{4} \cdot 17^{6} \cdot 131 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$53448$	$48$	$0$	$1$	$1$		$0$	$2949120$	$1.990698$	$19312898130234073/84888$	$0.98900$	$4.41881$	$[1, 0, 1, -1615372, 790101266]$	\(y^2+xy+y=x^3-1615372x+790101266\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 136.12.0.?, 408.24.0.?, $\ldots$	$[ ]$
227154.g2	227154p2	227154.g	227154p	$4$	$4$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{2} \cdot 17^{6} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$53448$	$48$	$0$	$1$	$1$		$2$	$1474560$	$1.644123$	$4722184089433/9884736$	$1.05106$	$3.74452$	$[1, 0, 1, -101012, 12325970]$	\(y^2+xy+y=x^3-101012x+12325970\)	2.6.0.a.1, 24.12.0.a.1, 136.12.0.?, 204.12.0.?, 408.24.0.?, $\ldots$	$[ ]$
227154.g3	227154p4	227154.g	227154p	$4$	$4$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{3} \cdot 3 \cdot 17^{6} \cdot 131^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$53448$	$48$	$0$	$1$	$4$	$2$	$0$	$2949120$	$1.990698$	$-1337180541913/7067998104$	$1.16620$	$3.82999$	$[1, 0, 1, -66332, 20926610]$	\(y^2+xy+y=x^3-66332x+20926610\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 136.12.0.?, 204.12.0.?, $\ldots$	$[ ]$
227154.g4	227154p1	227154.g	227154p	$4$	$4$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{12} \cdot 3 \cdot 17^{6} \cdot 131 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$53448$	$48$	$0$	$1$	$1$		$1$	$737280$	$1.297550$	$2845178713/1609728$	$0.95031$	$3.14335$	$[1, 0, 1, -8532, 44626]$	\(y^2+xy+y=x^3-8532x+44626\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 136.12.0.?, 204.12.0.?, $\ldots$	$[ ]$
227154.h1	227154q1	227154.h	227154q	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2 \cdot 3 \cdot 17^{6} \cdot 131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3144$	$2$	$0$	$7.653757382$	$1$		$0$	$201600$	$0.785108$	$68417929/786$	$0.83173$	$2.84110$	$[1, 0, 1, -2463, 46360]$	\(y^2+xy+y=x^3-2463x+46360\)	3144.2.0.?	$[(-1376/5, 19147/5)]$
227154.i1	227154r1	227154.i	227154r	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{3} \cdot 3^{7} \cdot 17^{6} \cdot 131 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3144$	$2$	$0$	$1$	$1$		$0$	$2604672$	$1.968491$	$4418129129836969/2291976$	$0.98193$	$4.29921$	$[1, 0, 1, -987953, -378047716]$	\(y^2+xy+y=x^3-987953x-378047716\)	3144.2.0.?	$[ ]$
227154.j1	227154s1	227154.j	227154s	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{6} \cdot 3^{3} \cdot 17^{6} \cdot 131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1572$	$2$	$0$	$1.967451038$	$1$		$2$	$1033344$	$1.482885$	$-2467489596697/226368$	$0.93723$	$3.69190$	$[1, 0, 1, -81360, 8926174]$	\(y^2+xy+y=x^3-81360x+8926174\)	1572.2.0.?	$[(161, 3)]$
227154.k1	227154g1	227154.k	227154g	$2$	$2$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{8} \cdot 3^{2} \cdot 17^{3} \cdot 131^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.32	2B	$106896$	$96$	$1$	$1$	$1$		$1$	$1241088$	$1.321173$	$3666012780227057/39538944$	$0.94438$	$3.59492$	$[1, 1, 1, -54610, -4934689]$	\(y^2+xy+y=x^3+x^2-54610x-4934689\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.q.1, 34.6.0.a.1, 68.12.0.k.1, $\ldots$	$[ ]$
227154.k2	227154g2	227154.k	227154g	$2$	$2$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{4} \cdot 3^{4} \cdot 17^{3} \cdot 131^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.28	2B	$106896$	$96$	$1$	$1$	$4$	$2$	$0$	$2482176$	$1.667747$	$-3398883618036977/381671897616$	$0.94642$	$3.60316$	$[1, 1, 1, -53250, -5190369]$	\(y^2+xy+y=x^3+x^2-53250x-5190369\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.t.1, 68.12.0.l.1, 136.24.0.?, $\ldots$	$[ ]$
227154.l1	227154h1	227154.l	227154h	$2$	$2$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{10} \cdot 3^{3} \cdot 17^{7} \cdot 131 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$53448$	$12$	$0$	$3.079011080$	$1$		$5$	$2350080$	$1.890848$	$211889947838113/61572096$	$0.89180$	$4.05293$	$[1, 1, 1, -358944, 82602561]$	\(y^2+xy+y=x^3+x^2-358944x+82602561\)	2.3.0.a.1, 8.6.0.d.1, 13362.6.0.?, 53448.12.0.?	$[(357, 165)]$
227154.l2	227154h2	227154.l	227154h	$2$	$2$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{5} \cdot 3^{6} \cdot 17^{8} \cdot 131^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$53448$	$12$	$0$	$1.539505540$	$1$		$6$	$4700160$	$2.237419$	$-140097562913953/115695892512$	$0.90218$	$4.09128$	$[1, 1, 1, -312704, 104723777]$	\(y^2+xy+y=x^3+x^2-312704x+104723777\)	2.3.0.a.1, 8.6.0.a.1, 26724.6.0.?, 53448.12.0.?	$[(545, 9553)]$
227154.m1	227154i2	227154.m	227154i	$2$	$5$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2 \cdot 3^{3} \cdot 17^{6} \cdot 131^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$267240$	$48$	$1$	$1$	$25$	$5$	$0$	$18480000$	$3.044682$	$1294373635812597347281/2083292441154$	$1.03042$	$5.31984$	$[1, 1, 1, -65616011, -204606903193]$	\(y^2+xy+y=x^3+x^2-65616011x-204606903193\)	5.12.0.a.2, 85.24.0.?, 3144.2.0.?, 15720.24.1.?, 267240.48.1.?	$[ ]$
227154.m2	227154i1	227154.m	227154i	$2$	$5$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{5} \cdot 3^{15} \cdot 17^{6} \cdot 131 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$267240$	$48$	$1$	$1$	$1$		$0$	$3696000$	$2.239964$	$1076291879750641/60150618144$	$0.97610$	$4.18471$	$[1, 1, 1, -617021, 177057587]$	\(y^2+xy+y=x^3+x^2-617021x+177057587\)	5.12.0.a.1, 85.24.0.?, 3144.2.0.?, 15720.24.1.?, 267240.48.1.?	$[ ]$
227154.n1	227154j1	227154.n	227154j	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{7} \cdot 3^{2} \cdot 17^{8} \cdot 131^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1048$	$2$	$0$	$1$	$1$		$0$	$8128512$	$2.430798$	$-6330906302194657/748452440448$	$0.91624$	$4.34345$	$[1, 1, 1, -1113812, 496049429]$	\(y^2+xy+y=x^3+x^2-1113812x+496049429\)	1048.2.0.?	$[ ]$
227154.o1	227154k1	227154.o	227154k	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{13} \cdot 3 \cdot 17^{2} \cdot 131^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$24$	$2$	$0$	$0.633731768$	$1$		$4$	$292032$	$0.806186$	$338342687/421748736$	$0.94976$	$2.67409$	$[1, 1, 1, 96, 16833]$	\(y^2+xy+y=x^3+x^2+96x+16833\)	24.2.0.b.1	$[(3, 129)]$
227154.p1	227154l1	227154.p	227154l	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{7} \cdot 3^{5} \cdot 17^{6} \cdot 131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3144$	$2$	$0$	$3.995198484$	$1$		$2$	$1447040$	$1.377943$	$8205738913/4074624$	$0.92368$	$3.22923$	$[1, 1, 1, -12144, 189009]$	\(y^2+xy+y=x^3+x^2-12144x+189009\)	3144.2.0.?	$[(-63, 873)]$
227154.q1	227154m1	227154.q	227154m	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{6} \cdot 3^{2} \cdot 17^{9} \cdot 131 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$4454$	$2$	$0$	$1$	$1$		$0$	$2350080$	$1.771421$	$-208527857/75456$	$0.80864$	$3.66000$	$[1, 1, 1, -60696, 7312281]$	\(y^2+xy+y=x^3+x^2-60696x+7312281\)	4454.2.0.?	$[ ]$
227154.r1	227154a1	227154.r	227154a	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{6} \cdot 3^{2} \cdot 17^{3} \cdot 131 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$4454$	$2$	$0$	$0.465162139$	$1$		$14$	$138240$	$0.354815$	$-208527857/75456$	$0.80864$	$2.28169$	$[1, 0, 0, -210, 1476]$	\(y^2+xy=x^3-210x+1476\)	4454.2.0.?	$[(24, 90), (-10, 56)]$
227154.s1	227154b1	227154.s	227154b	$2$	$2$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{3} \cdot 17^{6} \cdot 131 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$3144$	$12$	$0$	$1$	$1$		$1$	$1474560$	$1.285576$	$39616946929/226368$	$0.90388$	$3.35689$	$[1, 0, 0, -20525, -1127919]$	\(y^2+xy=x^3-20525x-1127919\)	2.3.0.a.1, 8.6.0.d.1, 786.6.0.?, 3144.12.0.?	$[ ]$
227154.s2	227154b2	227154.s	227154b	$2$	$2$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{3} \cdot 3^{6} \cdot 17^{6} \cdot 131^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$3144$	$12$	$0$	$1$	$1$		$0$	$2949120$	$1.632149$	$-3301293169/100082952$	$0.96192$	$3.47791$	$[1, 0, 0, -8965, -2387959]$	\(y^2+xy=x^3-8965x-2387959\)	2.3.0.a.1, 8.6.0.a.1, 1572.6.0.?, 3144.12.0.?	$[ ]$
227154.t1	227154c1	227154.t	227154c	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{13} \cdot 3 \cdot 17^{8} \cdot 131^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$24$	$2$	$0$	$1$	$1$		$0$	$4964544$	$2.222794$	$338342687/421748736$	$0.94976$	$4.05241$	$[1, 0, 0, 27738, 82507236]$	\(y^2+xy=x^3+27738x+82507236\)	24.2.0.b.1	$[ ]$
227154.u1	227154d1	227154.u	227154d	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{21} \cdot 3 \cdot 17^{6} \cdot 131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3144$	$2$	$0$	$2.264338415$	$1$		$2$	$2411136$	$1.939714$	$70593496254289/824180736$	$0.95961$	$3.96381$	$[1, 0, 0, -248835, 47271489]$	\(y^2+xy=x^3-248835x+47271489\)	3144.2.0.?	$[(110, 4553)]$
227154.v1	227154e1	227154.v	227154e	$2$	$2$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{8} \cdot 3^{2} \cdot 17^{9} \cdot 131^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.32	2B	$106896$	$96$	$1$	$1$	$4$	$2$	$1$	$21098496$	$2.737782$	$3666012780227057/39538944$	$0.94438$	$4.97323$	$[1, 0, 0, -15782296, -24133650112]$	\(y^2+xy=x^3-15782296x-24133650112\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.q.1, 34.6.0.a.1, 68.12.0.k.1, $\ldots$	$[ ]$
227154.v2	227154e2	227154.v	227154e	$2$	$2$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{4} \cdot 3^{4} \cdot 17^{9} \cdot 131^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.28	2B	$106896$	$96$	$1$	$1$	$4$	$2$	$0$	$42196992$	$3.084354$	$-3398883618036977/381671897616$	$0.94642$	$4.98148$	$[1, 0, 0, -15389256, -25392557232]$	\(y^2+xy=x^3-15389256x-25392557232\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.t.1, 68.12.0.l.1, 136.24.0.?, $\ldots$	$[ ]$
227154.w1	227154f1	227154.w	227154f	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( - 2^{3} \cdot 3^{4} \cdot 17^{6} \cdot 131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1048$	$2$	$0$	$1.557425731$	$1$		$2$	$737280$	$1.050417$	$109902239/84888$	$0.87261$	$2.87953$	$[1, 0, 0, 2884, 34728]$	\(y^2+xy=x^3+2884x+34728\)	1048.2.0.?	$[(262, 4204)]$

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