Elliptic curves over $\Q$ of conductor 51842

Results (32 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	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
51842.a1	51842l1	51842.a	51842l	$1$	$1$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{7} \cdot 7^{6} \cdot 23^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$8$	$2$	$0$	$5.863420982$	$1$		$2$	$6955200$	$2.897194$	$-97967097/128$	$1.09650$	$5.65890$	$[1, -1, 0, -16283248, 25323236224]$	\(y^2+xy=x^3-x^2-16283248x+25323236224\)	8.2.0.a.1	$[(1059, 95731)]$
51842.b1	51842k1	51842.b	51842k	$1$	$1$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{7} \cdot 7^{6} \cdot 23^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$8$	$2$	$0$	$4.679568705$	$1$		$2$	$302400$	$1.329445$	$-97967097/128$	$1.09650$	$3.92594$	$[1, -1, 0, -30781, -2073275]$	\(y^2+xy=x^3-x^2-30781x-2073275\)	8.2.0.a.1	$[(653, 15672)]$
51842.c1	51842j2	51842.c	51842j	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{2} \cdot 7^{3} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$644$	$12$	$0$	$6.544993497$	$1$		$2$	$540672$	$2.029182$	$13062552753151/92$	$0.97210$	$5.05266$	$[1, 0, 1, -1816862, -942758820]$	\(y^2+xy+y=x^3-1816862x-942758820\)	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 322.6.0.?, 644.12.0.?	$[(15224, 1863196)]$
51842.c2	51842j1	51842.c	51842j	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{4} \cdot 7^{3} \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$644$	$12$	$0$	$3.272496748$	$1$		$5$	$270336$	$1.682608$	$-3183010111/8464$	$0.90674$	$4.28671$	$[1, 0, 1, -113482, -14757396]$	\(y^2+xy+y=x^3-113482x-14757396\)	2.3.0.a.1, 14.6.0.b.1, 92.6.0.?, 644.12.0.?	$[(412, 2703)]$
51842.d1	51842i2	51842.d	51842i	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{7} \cdot 7^{8} \cdot 23^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$56$	$12$	$0$	$5.131314720$	$1$		$2$	$5677056$	$3.061455$	$24553362849625/1755162752$	$0.94866$	$5.64854$	$[1, 0, 1, -15695706, 22405989260]$	\(y^2+xy+y=x^3-15695706x+22405989260\)	2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1	$[(1026, 85408)]$
51842.d2	51842i1	51842.d	51842i	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{14} \cdot 7^{7} \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$56$	$12$	$0$	$2.565657360$	$1$		$3$	$2838528$	$2.714882$	$4533086375/60669952$	$0.94157$	$5.14187$	$[1, 0, 1, 893734, 1529837964]$	\(y^2+xy+y=x^3+893734x+1529837964\)	2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1	$[(9244, 889652)]$
51842.e1	51842c2	51842.e	51842c	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2 \cdot 7^{12} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1288$	$12$	$0$	$3.496456375$	$1$		$4$	$2433024$	$2.693710$	$1494447319737/5411854$	$1.04645$	$5.39070$	$[1, -1, 0, -6174058, 5887825950]$	\(y^2+xy=x^3-x^2-6174058x+5887825950\)	2.3.0.a.1, 28.6.0.c.1, 184.6.0.?, 1288.12.0.?	$[(1501, 43)]$
51842.e2	51842c1	51842.e	51842c	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{2} \cdot 7^{9} \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1288$	$12$	$0$	$1.748228187$	$1$		$7$	$1216512$	$2.347134$	$-60698457/725788$	$0.93405$	$4.74260$	$[1, -1, 0, -212228, 175200444]$	\(y^2+xy=x^3-x^2-212228x+175200444\)	2.3.0.a.1, 14.6.0.b.1, 184.6.0.?, 1288.12.0.?	$[(443, 12739)]$
51842.f1	51842b2	51842.f	51842b	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{2} \cdot 7^{10} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.11	2B	$1288$	$48$	$1$	$1.064217132$	$1$		$6$	$110592$	$1.338022$	$926859375/9604$	$1.05169$	$3.84390$	$[1, -1, 0, -22892, 1326884]$	\(y^2+xy=x^3-x^2-22892x+1326884\)	2.3.0.a.1, 4.12.0.f.1, 56.24.0.dj.1, 92.24.0.?, 1288.48.1.?	$[(-5, 1203)]$
51842.f2	51842b1	51842.f	51842b	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{4} \cdot 7^{8} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.27	2B	$1288$	$48$	$1$	$2.128434264$	$1$		$5$	$55296$	$0.991449$	$-3375/784$	$1.27623$	$3.24279$	$[1, -1, 0, -352, 51120]$	\(y^2+xy=x^3-x^2-352x+51120\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 28.12.0.n.1, 46.6.0.a.1, $\ldots$	$[(9, 216)]$
51842.g1	51842a2	51842.g	51842a	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{2} \cdot 7^{10} \cdot 23^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.11	2B	$1288$	$48$	$1$	$14.61722541$	$1$		$0$	$2543616$	$2.905769$	$926859375/9604$	$1.05169$	$5.57687$	$[1, -1, 0, -12109967, -16071538015]$	\(y^2+xy=x^3-x^2-12109967x-16071538015\)	2.3.0.a.1, 4.12.0.f.1, 56.24.0.dj.1, 92.24.0.?, 1288.48.1.?	$[(-22380287/107, 15077757610/107)]$
51842.g2	51842a1	51842.g	51842a	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{4} \cdot 7^{8} \cdot 23^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.27	2B	$1288$	$48$	$1$	$29.23445082$	$1$		$1$	$1271808$	$2.559196$	$-3375/784$	$1.27623$	$4.97575$	$[1, -1, 0, -186307, -620859387]$	\(y^2+xy=x^3-x^2-186307x-620859387\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 28.12.0.n.1, 46.6.0.a.1, $\ldots$	$[(30401250181647/88061, 164379297772215579927/88061)]$
51842.h1	51842d2	51842.h	51842d	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{5} \cdot 7^{6} \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$184$	$12$	$0$	$13.32584770$	$1$		$0$	$1520640$	$2.448795$	$545138290809/16928$	$1.08081$	$5.29780$	$[1, -1, 0, -4411430, -3565096172]$	\(y^2+xy=x^3-x^2-4411430x-3565096172\)	2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.?	$[(-26964951/149, 1084697522/149)]$
51842.h2	51842d1	51842.h	51842d	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{10} \cdot 7^{6} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$184$	$12$	$0$	$26.65169541$	$1$		$1$	$760320$	$2.102219$	$-116930169/23552$	$1.03422$	$4.54720$	$[1, -1, 0, -264070, -60576972]$	\(y^2+xy=x^3-x^2-264070x-60576972\)	2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.?	$[(1996938064109/45445, 2229339021506297462/45445)]$
51842.i1	51842h2	51842.i	51842h	$2$	$3$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{6} \cdot 7^{6} \cdot 23^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$84$	$32$	$0$	$4.539703557$	$1$		$2$	$1987200$	$2.407383$	$-313994137/64$	$0.96923$	$5.18836$	$[1, 1, 0, -2968494, 1967687156]$	\(y^2+xy=x^3+x^2-2968494x+1967687156\)	3.4.0.a.1, 4.2.0.a.1, 12.16.0.b.2, 21.8.0-3.a.1.2, 28.4.0-4.a.1.1, $\ldots$	$[(1004, 290)]$
51842.i2	51842h1	51842.i	51842h	$2$	$3$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{2} \cdot 7^{6} \cdot 23^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$84$	$32$	$0$	$1.513234519$	$1$		$2$	$662400$	$1.858076$	$23/4$	$0.94596$	$4.20019$	$[1, 1, 0, 12421, 9226001]$	\(y^2+xy=x^3+x^2+12421x+9226001\)	3.4.0.a.1, 4.2.0.a.1, 12.16.0.b.1, 21.8.0-3.a.1.1, 28.4.0-4.a.1.1, $\ldots$	$[(220, 4651)]$
51842.j1	51842e6	51842.j	51842e	$6$	$18$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{9} \cdot 7^{8} \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$11592$	$864$	$21$	$34.03556686$	$1$		$0$	$3649536$	$2.953804$	$2251439055699625/25088$	$1.06489$	$6.06476$	$[1, 1, 0, -70777830, -229218601324]$	\(y^2+xy=x^3+x^2-70777830x-229218601324\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$	$[(13905333620359879/5910, 1639688070309056853955297/5910)]$
51842.j2	51842e5	51842.j	51842e	$6$	$18$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{18} \cdot 7^{7} \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$11592$	$864$	$21$	$17.01778343$	$1$		$1$	$1824768$	$2.607231$	$-548347731625/1835008$	$1.02933$	$5.29888$	$[1, 1, 0, -4420070, -3588945772]$	\(y^2+xy=x^3+x^2-4420070x-3588945772\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$	$[(376918183/394, -33569930741/394)]$
51842.j3	51842e4	51842.j	51842e	$6$	$18$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{3} \cdot 7^{12} \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.12.0.1	2B, 3Cs	$11592$	$864$	$21$	$11.34518895$	$1$		$0$	$1216512$	$2.404495$	$4956477625/941192$	$1.00821$	$4.86483$	$[1, 1, 0, -920735, -279119203]$	\(y^2+xy=x^3+x^2-920735x-279119203\)	2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 24.72.1.h.1, $\ldots$	$[(1465231/30, 1338860281/30)]$
51842.j4	51842e2	51842.j	51842e	$6$	$18$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2 \cdot 7^{8} \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$11592$	$864$	$21$	$3.781729651$	$1$		$2$	$405504$	$1.855190$	$128787625/98$	$0.96763$	$4.52858$	$[1, 1, 0, -272710, 54665514]$	\(y^2+xy=x^3+x^2-272710x+54665514\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$	$[(-477, 8985)]$
51842.j5	51842e1	51842.j	51842e	$6$	$18$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{2} \cdot 7^{7} \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$11592$	$864$	$21$	$1.890864825$	$1$		$3$	$202752$	$1.508617$	$-15625/28$	$1.01712$	$3.82787$	$[1, 1, 0, -13500, 1216412]$	\(y^2+xy=x^3+x^2-13500x+1216412\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$	$[(59, 764)]$
51842.j6	51842e3	51842.j	51842e	$6$	$18$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{6} \cdot 7^{9} \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.12.0.1	2B, 3Cs	$11592$	$864$	$21$	$5.672594476$	$1$		$1$	$608256$	$2.057922$	$9938375/21952$	$0.98695$	$4.38800$	$[1, 1, 0, 116105, -25508139]$	\(y^2+xy=x^3+x^2+116105x-25508139\)	2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$	$[(5871/2, 454359/2)]$
51842.k1	51842f2	51842.k	51842f	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{2} \cdot 7^{9} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$644$	$12$	$0$	$18.78251966$	$1$		$0$	$3784704$	$3.002136$	$13062552753151/92$	$0.97210$	$6.12815$	$[1, 1, 0, -89026214, 323277248960]$	\(y^2+xy=x^3+x^2-89026214x+323277248960\)	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 322.6.0.?, 644.12.0.?	$[(31935814807/2394, 182110642557031/2394)]$
51842.k2	51842f1	51842.k	51842f	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{4} \cdot 7^{9} \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$644$	$12$	$0$	$9.391259834$	$1$		$1$	$1892352$	$2.655563$	$-3183010111/8464$	$0.90674$	$5.36220$	$[1, 1, 0, -5560594, 5056226148]$	\(y^2+xy=x^3+x^2-5560594x+5056226148\)	2.3.0.a.1, 14.6.0.b.1, 92.6.0.?, 644.12.0.?	$[(138639/14, 104504721/14)]$
51842.l1	51842g2	51842.l	51842g	$2$	$3$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{6} \cdot 7^{6} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$1932$	$32$	$0$	$7.133767858$	$1$		$0$	$86400$	$0.839635$	$-313994137/64$	$0.96923$	$3.45540$	$[1, 1, 0, -5611, -164163]$	\(y^2+xy=x^3+x^2-5611x-164163\)	3.4.0.a.1, 4.2.0.a.1, 12.16.0.b.2, 483.8.0.?, 644.4.0.?, $\ldots$	$[(2454/5, 55473/5)]$
51842.l2	51842g1	51842.l	51842g	$2$	$3$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{2} \cdot 7^{6} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$1932$	$32$	$0$	$2.377922619$	$1$		$2$	$28800$	$0.290329$	$23/4$	$0.94596$	$2.46723$	$[1, 1, 0, 24, -748]$	\(y^2+xy=x^3+x^2+24x-748\)	3.4.0.a.1, 4.2.0.a.1, 12.16.0.b.1, 483.8.0.?, 644.4.0.?, $\ldots$	$[(8, 2)]$
51842.m1	51842p2	51842.m	51842p	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2 \cdot 7^{8} \cdot 23^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$1288$	$12$	$0$	$1$	$1$		$0$	$1216512$	$2.166012$	$304821217/51842$	$0.85015$	$4.60795$	$[1, 0, 0, -363434, -70893950]$	\(y^2+xy=x^3-363434x-70893950\)	2.3.0.a.1, 8.6.0.b.1, 644.6.0.?, 1288.12.0.?	$[]$
51842.m2	51842p1	51842.m	51842p	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{2} \cdot 7^{7} \cdot 23^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$		$1$	$608256$	$1.819439$	$7189057/644$	$0.79155$	$4.26277$	$[1, 0, 0, -104224, 11897724]$	\(y^2+xy=x^3-104224x+11897724\)	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$
51842.n1	51842n1	51842.n	51842n	$1$	$1$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{7} \cdot 7^{8} \cdot 23^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$		$0$	$2225664$	$2.480450$	$8947391/6272$	$1.06774$	$4.86058$	$[1, 0, 0, 906695, 152830201]$	\(y^2+xy=x^3+906695x+152830201\)	8.2.0.a.1	$[]$
51842.o1	51842m1	51842.o	51842m	$1$	$1$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{7} \cdot 7^{8} \cdot 23^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$		$0$	$96768$	$0.912702$	$8947391/6272$	$1.06774$	$3.12762$	$[1, 0, 0, 1714, -12412]$	\(y^2+xy=x^3+1714x-12412\)	8.2.0.a.1	$[]$
51842.p1	51842o2	51842.p	51842o	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{5} \cdot 7^{8} \cdot 23^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$1288$	$12$	$0$	$1$	$1$		$0$	$2027520$	$2.579353$	$582810602977/829472$	$0.91997$	$5.30396$	$[1, 1, 1, -4510794, 3681045815]$	\(y^2+xy+y=x^3+x^2-4510794x+3681045815\)	2.3.0.a.1, 8.6.0.b.1, 644.6.0.?, 1288.12.0.?	$[]$
51842.p2	51842o1	51842.p	51842o	$2$	$2$	\( 2 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{10} \cdot 7^{7} \cdot 23^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$		$1$	$1013760$	$2.232780$	$304821217/164864$	$0.89657$	$4.60795$	$[1, 1, 1, -363434, 21415351]$	\(y^2+xy+y=x^3+x^2-363434x+21415351\)	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$