Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (40 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
570.b1	570a2	570.b	570a	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 19 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$0.311649543$	$1$		$10$	$384$	$0.443991$	$468898230633769/5540400$	$[1, 1, 0, -1618, 24388]$	\(y^2+xy=x^3+x^2-1618x+24388\)
1710.s1	1710r2	1710.s	1710r	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$3072$	$0.993297$	$468898230633769/5540400$	$[1, -1, 1, -14567, -673041]$	\(y^2+xy+y=x^3-x^2-14567x-673041\)
2850.y1	2850x2	2850.y	2850x	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.218945384$	$1$		$10$	$9216$	$1.248711$	$468898230633769/5540400$	$[1, 0, 0, -40463, 3129417]$	\(y^2+xy=x^3-40463x+3129417\)
4560.r1	4560z2	4560.r	4560z	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 19 \)	\( 2^{16} \cdot 3^{6} \cdot 5^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$9216$	$1.137138$	$468898230633769/5540400$	$[0, 1, 0, -25896, -1612620]$	\(y^2=x^3+x^2-25896x-1612620\)
8550.g1	8550f2	8550.g	8550f	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$73728$	$1.798016$	$468898230633769/5540400$	$[1, -1, 0, -364167, -84494259]$	\(y^2+xy=x^3-x^2-364167x-84494259\)
10830.bd1	10830bc2	10830.bd	10830bc	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$138240$	$1.916210$	$468898230633769/5540400$	$[1, 0, 0, -584286, -171951084]$	\(y^2+xy=x^3-584286x-171951084\)
13680.bd1	13680bw2	13680.bd	13680bw	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{16} \cdot 3^{12} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.726876703$	$1$		$5$	$73728$	$1.686443$	$468898230633769/5540400$	$[0, 0, 0, -233067, 43307674]$	\(y^2=x^3-233067x+43307674\)
18240.v1	18240ce2	18240.v	18240ce	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 19 \)	\( 2^{22} \cdot 3^{6} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.460480331$	$1$		$3$	$73728$	$1.483711$	$468898230633769/5540400$	$[0, -1, 0, -103585, -12797375]$	\(y^2=x^3-x^2-103585x-12797375\)
18240.cy1	18240bp2	18240.cy	18240bp	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 19 \)	\( 2^{22} \cdot 3^{6} \cdot 5^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$73728$	$1.483711$	$468898230633769/5540400$	$[0, 1, 0, -103585, 12797375]$	\(y^2=x^3+x^2-103585x+12797375\)
22800.bj1	22800ce2	22800.bj	22800ce	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{6} \cdot 5^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8.053000506$	$1$		$1$	$221184$	$1.941856$	$468898230633769/5540400$	$[0, -1, 0, -647408, -200282688]$	\(y^2=x^3-x^2-647408x-200282688\)
27930.bn1	27930bz2	27930.bn	27930bz	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 7^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.404364615$	$1$		$6$	$138240$	$1.416946$	$468898230633769/5540400$	$[1, 0, 1, -79308, -8602982]$	\(y^2+xy+y=x^3-79308x-8602982\)
32490.y1	32490x2	32490.y	32490x	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$1105920$	$2.465515$	$468898230633769/5540400$	$[1, -1, 0, -5258574, 4642679268]$	\(y^2+xy=x^3-x^2-5258574x+4642679268\)
54150.c1	54150i2	54150.c	54150i	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 19^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 5^{8} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$3317760$	$2.720928$	$468898230633769/5540400$	$[1, 1, 0, -14607150, -21493885500]$	\(y^2+xy=x^3+x^2-14607150x-21493885500\)
54720.z1	54720dq2	54720.z	54720dq	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{22} \cdot 3^{12} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.596384146$	$1$		$7$	$589824$	$2.033016$	$468898230633769/5540400$	$[0, 0, 0, -932268, 346461392]$	\(y^2=x^3-932268x+346461392\)
54720.bm1	54720bg2	54720.bm	54720bg	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{22} \cdot 3^{12} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8.007880389$	$1$		$1$	$589824$	$2.033016$	$468898230633769/5540400$	$[0, 0, 0, -932268, -346461392]$	\(y^2=x^3-932268x-346461392\)
68400.eo1	68400fi2	68400.eo	68400fi	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{12} \cdot 5^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1769472$	$2.491161$	$468898230633769/5540400$	$[0, 0, 0, -5826675, 5413459250]$	\(y^2=x^3-5826675x+5413459250\)
68970.bk1	68970bq2	68970.bk	68970bq	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 11^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$414720$	$1.642939$	$468898230633769/5540400$	$[1, 1, 1, -195841, -33439537]$	\(y^2+xy+y=x^3+x^2-195841x-33439537\)
83790.el1	83790et2	83790.el	83790et	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 7^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.480134087$	$1$		$4$	$1105920$	$1.966251$	$468898230633769/5540400$	$[1, -1, 1, -713768, 232280507]$	\(y^2+xy+y=x^3-x^2-713768x+232280507\)
86640.h1	86640cc2	86640.h	86640cc	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 19^{2} \)	\( 2^{16} \cdot 3^{6} \cdot 5^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.640099132$	$1$		$3$	$3317760$	$2.609356$	$468898230633769/5540400$	$[0, -1, 0, -9348576, 11004869376]$	\(y^2=x^3-x^2-9348576x+11004869376\)
91200.bs1	91200bi2	91200.bs	91200bi	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 19 \)	\( 2^{22} \cdot 3^{6} \cdot 5^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1769472$	$2.288429$	$468898230633769/5540400$	$[0, -1, 0, -2589633, 1604851137]$	\(y^2=x^3-x^2-2589633x+1604851137\)
91200.ht1	91200hr2	91200.ht	91200hr	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 19 \)	\( 2^{22} \cdot 3^{6} \cdot 5^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.900118294$	$1$		$3$	$1769472$	$2.288429$	$468898230633769/5540400$	$[0, 1, 0, -2589633, -1604851137]$	\(y^2=x^3+x^2-2589633x-1604851137\)
96330.cm1	96330ct2	96330.cm	96330ct	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 13^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$903168$	$1.726465$	$468898230633769/5540400$	$[1, 1, 1, -273530, 54947927]$	\(y^2+xy+y=x^3+x^2-273530x+54947927\)
139650.em1	139650dq2	139650.em	139650dq	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{8} \cdot 7^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$3317760$	$2.221664$	$468898230633769/5540400$	$[1, 1, 1, -1982688, -1075372719]$	\(y^2+xy+y=x^3+x^2-1982688x-1075372719\)
162450.dl1	162450bb2	162450.dl	162450bb	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{4} \cdot 3^{12} \cdot 5^{8} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$26542080$	$3.270237$	$468898230633769/5540400$	$[1, -1, 1, -131464355, 580203444147]$	\(y^2+xy+y=x^3-x^2-131464355x+580203444147\)
164730.bs1	164730bo2	164730.bs	164730bo	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 17^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 17^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.613815550$	$1$		$8$	$1966080$	$1.860598$	$468898230633769/5540400$	$[1, 0, 1, -467753, 123092156]$	\(y^2+xy+y=x^3-467753x+123092156\)
206910.bq1	206910ct2	206910.bq	206910ct	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 11^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.487512967$	$1$		$4$	$3317760$	$2.192245$	$468898230633769/5540400$	$[1, -1, 0, -1762569, 901104925]$	\(y^2+xy=x^3-x^2-1762569x+901104925\)
223440.dn1	223440dx2	223440.dn	223440dx	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{6} \cdot 5^{2} \cdot 7^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$3317760$	$2.110092$	$468898230633769/5540400$	$[0, -1, 0, -1268920, 550590832]$	\(y^2=x^3-x^2-1268920x+550590832\)
259920.ee1	259920ee2	259920.ee	259920ee	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{16} \cdot 3^{12} \cdot 5^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6.448039373$	$1$		$1$	$26542080$	$3.158665$	$468898230633769/5540400$	$[0, 0, 0, -84137187, -297047335966]$	\(y^2=x^3-84137187x-297047335966\)
273600.dc1	273600dc2	273600.dc	273600dc	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{22} \cdot 3^{12} \cdot 5^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$7.768991981$	$1$		$3$	$14155776$	$2.837738$	$468898230633769/5540400$	$[0, 0, 0, -23306700, -43307674000]$	\(y^2=x^3-23306700x-43307674000\)
273600.ni1	273600ni2	273600.ni	273600ni	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{22} \cdot 3^{12} \cdot 5^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.324676394$	$1$		$5$	$14155776$	$2.837738$	$468898230633769/5540400$	$[0, 0, 0, -23306700, 43307674000]$	\(y^2=x^3-23306700x+43307674000\)
288990.j1	288990j2	288990.j	288990j	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 13^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.938283270$	$1$		$4$	$7225344$	$2.275772$	$468898230633769/5540400$	$[1, -1, 0, -2461770, -1486055804]$	\(y^2+xy=x^3-x^2-2461770x-1486055804\)
301530.l1	301530l2	301530.l	301530l	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 19 \cdot 23^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 19 \cdot 23^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$4730880$	$2.011738$	$468898230633769/5540400$	$[1, 1, 0, -856197, -305289891]$	\(y^2+xy=x^3+x^2-856197x-305289891\)
344850.dl1	344850dl2	344850.dl	344850dl	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{8} \cdot 11^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$9953280$	$2.447659$	$468898230633769/5540400$	$[1, 0, 1, -4896026, -4170150052]$	\(y^2+xy+y=x^3-4896026x-4170150052\)
346560.ff1	346560ff2	346560.ff	346560ff	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 19^{2} \)	\( 2^{22} \cdot 3^{6} \cdot 5^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$21.07175142$	$1$		$1$	$26542080$	$2.955933$	$468898230633769/5540400$	$[0, -1, 0, -37394305, -88001560703]$	\(y^2=x^3-x^2-37394305x-88001560703\)
346560.ix1	346560ix2	346560.ix	346560ix	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 19^{2} \)	\( 2^{22} \cdot 3^{6} \cdot 5^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.714515827$	$1$		$7$	$26542080$	$2.955933$	$468898230633769/5540400$	$[0, 1, 0, -37394305, 88001560703]$	\(y^2=x^3+x^2-37394305x+88001560703\)
418950.ir1	418950ir2	418950.ir	418950ir	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{8} \cdot 7^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$26542080$	$2.770969$	$468898230633769/5540400$	$[1, -1, 0, -17844192, 29017219216]$	\(y^2+xy=x^3-x^2-17844192x+29017219216\)
433200.kb1	433200kb2	433200.kb	433200kb	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 19^{2} \)	\( 2^{16} \cdot 3^{6} \cdot 5^{8} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$79626240$	$3.414078$	$468898230633769/5540400$	$[0, 1, 0, -233714408, 1375141243188]$	\(y^2=x^3+x^2-233714408x+1375141243188\)
479370.cu1	479370cu2	479370.cu	479370cu	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 19 \cdot 29^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 19 \cdot 29^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$8988672$	$2.127640$	$468898230633769/5540400$	$[1, 0, 0, -1361176, 611131280]$	\(y^2+xy=x^3-1361176x+611131280\)
481650.dz1	481650dz2	481650.dz	481650dz	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{8} \cdot 13^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.541733001$	$1$		$4$	$21676032$	$2.531185$	$468898230633769/5540400$	$[1, 0, 1, -6838251, 6882167398]$	\(y^2+xy+y=x^3-6838251x+6882167398\)
494190.db1	494190db2	494190.db	494190db	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 17^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 17^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.402217979$	$1$		$4$	$15728640$	$2.409904$	$468898230633769/5540400$	$[1, -1, 1, -4209773, -3323488219]$	\(y^2+xy+y=x^3-x^2-4209773x-3323488219\)