Elliptic curve search results

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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
256.a1	256a2	256.a	256a	$2$	$2$	$2^{8}$	$2^{15}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓	$2$	16.192.5.624	2B				$0.960251595$	$1$		$5$	$16$	$-0.403973$	$8000$	$0.90298$	$3.49572$	$[0, 1, 0, -13, -21]$	$y^2=x^3+x^2-13x-21$		$[(5, 8)]$
256.a2	256a1	256.a	256a	$2$	$2$	$2^{8}$	$2^{9}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓	$2$	16.192.5.607	2B				$0.480125797$	$1$		$7$	$8$	$-0.750546$	$8000$	$0.90298$	$2.74572$	$[0, 1, 0, -3, 1]$	$y^2=x^3+x^2-3x+1$		$[(0, 1)]$
256.d1	256d2	256.d	256d	$2$	$2$	$2^{8}$	$2^{15}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓	$2$	16.192.5.602	2B				$1$	$1$		$1$	$16$	$-0.403973$	$8000$	$0.90298$	$3.49572$	$[0, -1, 0, -13, 21]$	$y^2=x^3-x^2-13x+21$		$[]$
256.d2	256d1	256.d	256d	$2$	$2$	$2^{8}$	$2^{9}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓	$2$	16.192.5.617	2B				$1$	$1$		$1$	$8$	$-0.750546$	$8000$	$0.90298$	$2.74572$	$[0, -1, 0, -3, -1]$	$y^2=x^3-x^2-3x-1$		$[]$
2304.h1	2304k2	2304.h	2304k	$2$	$2$	$2^{8} \cdot 3^{2}$	$2^{15} \cdot 3^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$2.112877375$	$1$		$5$	$384$	$0.145334$	$8000$	$0.90298$	$3.35504$	$[0, 0, 0, -120, -448]$	$y^2=x^3-120x-448$		$[(-7, 7)]$
2304.h2	2304k1	2304.h	2304k	$2$	$2$	$2^{8} \cdot 3^{2}$	$2^{9} \cdot 3^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1.056438687$	$1$		$5$	$192$	$-0.201240$	$8000$	$0.90298$	$2.81788$	$[0, 0, 0, -30, 56]$	$y^2=x^3-30x+56$		$[(2, 2)]$
2304.i1	2304c2	2304.i	2304c	$2$	$2$	$2^{8} \cdot 3^{2}$	$2^{15} \cdot 3^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$384$	$0.145334$	$8000$	$0.90298$	$3.35504$	$[0, 0, 0, -120, 448]$	$y^2=x^3-120x+448$		$[]$
2304.i2	2304c1	2304.i	2304c	$2$	$2$	$2^{8} \cdot 3^{2}$	$2^{9} \cdot 3^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$192$	$-0.201240$	$8000$	$0.90298$	$2.81788$	$[0, 0, 0, -30, -56]$	$y^2=x^3-30x-56$		$[]$
6400.a1	6400r2	6400.a	6400r	$2$	$2$	$2^{8} \cdot 5^{2}$	$2^{15} \cdot 5^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$2304$	$0.400746$	$8000$	$0.90298$	$3.31365$	$[0, 1, 0, -333, 1963]$	$y^2=x^3+x^2-333x+1963$		$[]$
6400.a2	6400r1	6400.a	6400r	$2$	$2$	$2^{8} \cdot 5^{2}$	$2^{9} \cdot 5^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$1152$	$0.054173$	$8000$	$0.90298$	$2.83911$	$[0, 1, 0, -83, -287]$	$y^2=x^3+x^2-83x-287$		$[]$
6400.x1	6400f2	6400.x	6400f	$2$	$2$	$2^{8} \cdot 5^{2}$	$2^{15} \cdot 5^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$4.759367983$	$1$		$1$	$2304$	$0.400746$	$8000$	$0.90298$	$3.31365$	$[0, -1, 0, -333, -1963]$	$y^2=x^3-x^2-333x-1963$		$[(-68/3, 217/3)]$
6400.x2	6400f1	6400.x	6400f	$2$	$2$	$2^{8} \cdot 5^{2}$	$2^{9} \cdot 5^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$2.379683991$	$1$		$3$	$1152$	$0.054173$	$8000$	$0.90298$	$2.83911$	$[0, -1, 0, -83, 287]$	$y^2=x^3-x^2-83x+287$		$[(-2, 21)]$
12544.c1	12544o2	12544.c	12544o	$2$	$2$	$2^{8} \cdot 7^{2}$	$2^{15} \cdot 7^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1.854270723$	$1$		$5$	$6144$	$0.568982$	$8000$	$0.90298$	$3.29129$	$[0, 1, 0, -653, -5909]$	$y^2=x^3+x^2-653x-5909$		$[(-11, 8)]$
12544.c2	12544o1	12544.c	12544o	$2$	$2$	$2^{8} \cdot 7^{2}$	$2^{9} \cdot 7^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$0.927135361$	$1$		$7$	$3072$	$0.222409$	$8000$	$0.90298$	$2.85059$	$[0, 1, 0, -163, 657]$	$y^2=x^3+x^2-163x+657$		$[(16, 49)]$
12544.n1	12544d2	12544.n	12544d	$2$	$2$	$2^{8} \cdot 7^{2}$	$2^{15} \cdot 7^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$6144$	$0.568982$	$8000$	$0.90298$	$3.29129$	$[0, -1, 0, -653, 5909]$	$y^2=x^3-x^2-653x+5909$		$[]$
12544.n2	12544d1	12544.n	12544d	$2$	$2$	$2^{8} \cdot 7^{2}$	$2^{9} \cdot 7^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$3072$	$0.222409$	$8000$	$0.90298$	$2.85059$	$[0, -1, 0, -163, -657]$	$y^2=x^3-x^2-163x-657$		$[]$
30976.a1	30976d2	30976.a	30976d	$2$	$2$	$2^{8} \cdot 11^{2}$	$2^{15} \cdot 11^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$17280$	$0.794975$	$8000$	$0.90298$	$3.26582$	$[0, 1, 0, -1613, 21547]$	$y^2=x^3+x^2-1613x+21547$		$[]$
30976.a2	30976d1	30976.a	30976d	$2$	$2$	$2^{8} \cdot 11^{2}$	$2^{9} \cdot 11^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$8640$	$0.448401$	$8000$	$0.90298$	$2.86365$	$[0, 1, 0, -403, -2895]$	$y^2=x^3+x^2-403x-2895$		$[]$
30976.h1	30976h2	30976.h	30976h	$2$	$2$	$2^{8} \cdot 11^{2}$	$2^{15} \cdot 11^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$10.76473485$	$1$		$3$	$17280$	$0.794975$	$8000$	$0.90298$	$3.26582$	$[0, -1, 0, -1613, -21547]$	$y^2=x^3-x^2-1613x-21547$		$[(1472299, 1786462392)]$
30976.h2	30976h1	30976.h	30976h	$2$	$2$	$2^{8} \cdot 11^{2}$	$2^{9} \cdot 11^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$5.382367428$	$1$		$1$	$8640$	$0.448401$	$8000$	$0.90298$	$2.86365$	$[0, -1, 0, -403, 2895]$	$y^2=x^3-x^2-403x+2895$		$[(-203/3, 26/3)]$
43264.c1	43264f2	43264.c	43264f	$2$	$2$	$2^{8} \cdot 13^{2}$	$2^{15} \cdot 13^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$5.769753780$	$1$		$1$	$37632$	$0.878502$	$8000$	$0.90298$	$3.25750$	$[0, 1, 0, -2253, -37205]$	$y^2=x^3+x^2-2253x-37205$		$[(-266/3, 1799/3)]$
43264.c2	43264f1	43264.c	43264f	$2$	$2$	$2^{8} \cdot 13^{2}$	$2^{9} \cdot 13^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$2.884876890$	$1$		$3$	$18816$	$0.531928$	$8000$	$0.90298$	$2.86792$	$[0, 1, 0, -563, 4369]$	$y^2=x^3+x^2-563x+4369$		$[(8, 21)]$
43264.z1	43264t2	43264.z	43264t	$2$	$2$	$2^{8} \cdot 13^{2}$	$2^{15} \cdot 13^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$37632$	$0.878502$	$8000$	$0.90298$	$3.25750$	$[0, -1, 0, -2253, 37205]$	$y^2=x^3-x^2-2253x+37205$		$[]$
43264.z2	43264t1	43264.z	43264t	$2$	$2$	$2^{8} \cdot 13^{2}$	$2^{9} \cdot 13^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$18816$	$0.531928$	$8000$	$0.90298$	$2.86792$	$[0, -1, 0, -563, -4369]$	$y^2=x^3-x^2-563x-4369$		$[]$
57600.bk1	57600cn2	57600.bk	57600cn	$2$	$2$	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{15} \cdot 3^{6} \cdot 5^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$3.742756077$	$1$		$5$	$55296$	$0.950052$	$8000$	$0.90298$	$3.25078$	$[0, 0, 0, -3000, -56000]$	$y^2=x^3-3000x-56000$		$[(-39, 41)]$
57600.bk2	57600cn1	57600.bk	57600cn	$2$	$2$	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{9} \cdot 3^{6} \cdot 5^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1.871378038$	$1$		$5$	$27648$	$0.603478$	$8000$	$0.90298$	$2.87136$	$[0, 0, 0, -750, 7000]$	$y^2=x^3-750x+7000$		$[(11, 9)]$
57600.ch1	57600r2	57600.ch	57600r	$2$	$2$	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{15} \cdot 3^{6} \cdot 5^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$55296$	$0.950052$	$8000$	$0.90298$	$3.25078$	$[0, 0, 0, -3000, 56000]$	$y^2=x^3-3000x+56000$		$[]$
57600.ch2	57600r1	57600.ch	57600r	$2$	$2$	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{9} \cdot 3^{6} \cdot 5^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$27648$	$0.603478$	$8000$	$0.90298$	$2.87136$	$[0, 0, 0, -750, -7000]$	$y^2=x^3-750x-7000$		$[]$
73984.a1	73984p2	73984.a	73984p	$2$	$2$	$2^{8} \cdot 17^{2}$	$2^{15} \cdot 17^{6}$	$2$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$4.167180624$	$1$		$11$	$73728$	$1.012634$	$8000$	$0.90298$	$3.24518$	$[0, 1, 0, -3853, 80235]$	$y^2=x^3+x^2-3853x+80235$		$[(62, 289), (470, 10115)]$
73984.a2	73984p1	73984.a	73984p	$2$	$2$	$2^{8} \cdot 17^{2}$	$2^{9} \cdot 17^{6}$	$2$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$4.167180624$	$1$		$5$	$36864$	$0.666060$	$8000$	$0.90298$	$2.87424$	$[0, 1, 0, -963, -10511]$	$y^2=x^3+x^2-963x-10511$		$[(113, 1156), (-15, 28)]$
73984.p1	73984h2	73984.p	73984h	$2$	$2$	$2^{8} \cdot 17^{2}$	$2^{15} \cdot 17^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$2.127068217$	$4$	$2$	$3$	$73728$	$1.012634$	$8000$	$0.90298$	$3.24518$	$[0, -1, 0, -3853, -80235]$	$y^2=x^3-x^2-3853x-80235$		$[(108, 867)]$
73984.p2	73984h1	73984.p	73984h	$2$	$2$	$2^{8} \cdot 17^{2}$	$2^{9} \cdot 17^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$4.254136434$	$1$		$3$	$36864$	$0.666060$	$8000$	$0.90298$	$2.87424$	$[0, -1, 0, -963, 10511]$	$y^2=x^3-x^2-963x+10511$		$[(95, 876)]$
92416.c1	92416bt2	92416.c	92416bt	$2$	$2$	$2^{8} \cdot 19^{2}$	$2^{15} \cdot 19^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$7.155820499$	$1$		$1$	$114048$	$1.068247$	$8000$	$0.90298$	$3.24041$	$[0, 1, 0, -4813, -115413]$	$y^2=x^3+x^2-4813x-115413$		$[(-986/5, 15113/5)]$
92416.c2	92416bt1	92416.c	92416bt	$2$	$2$	$2^{8} \cdot 19^{2}$	$2^{9} \cdot 19^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$3.577910249$	$1$		$3$	$57024$	$0.721673$	$8000$	$0.90298$	$2.87668$	$[0, 1, 0, -1203, 13825]$	$y^2=x^3+x^2-1203x+13825$		$[(-25, 170)]$
92416.bt1	92416v2	92416.bt	92416v	$2$	$2$	$2^{8} \cdot 19^{2}$	$2^{15} \cdot 19^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$114048$	$1.068247$	$8000$	$0.90298$	$3.24041$	$[0, -1, 0, -4813, 115413]$	$y^2=x^3-x^2-4813x+115413$		$[]$
92416.bt2	92416v1	92416.bt	92416v	$2$	$2$	$2^{8} \cdot 19^{2}$	$2^{9} \cdot 19^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$57024$	$0.721673$	$8000$	$0.90298$	$2.87668$	$[0, -1, 0, -1203, -13825]$	$y^2=x^3-x^2-1203x-13825$		$[]$
112896.bz1	112896dm2	112896.bz	112896dm	$2$	$2$	$2^{8} \cdot 3^{2} \cdot 7^{2}$	$2^{15} \cdot 3^{6} \cdot 7^{6}$	$2$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$3.589260903$	$1$		$11$	$147456$	$1.118288$	$8000$	$0.90298$	$3.23627$	$[0, 0, 0, -5880, 153664]$	$y^2=x^3-5880x+153664$		$[(0, 392), (105, 833)]$
112896.bz2	112896dm1	112896.bz	112896dm	$2$	$2$	$2^{8} \cdot 3^{2} \cdot 7^{2}$	$2^{9} \cdot 3^{6} \cdot 7^{6}$	$2$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$3.589260903$	$1$		$13$	$73728$	$0.771715$	$8000$	$0.90298$	$2.87880$	$[0, 0, 0, -1470, -19208]$	$y^2=x^3-1470x-19208$		$[(-21, 49), (44, 36)]$
112896.ci1	112896bi2	112896.ci	112896bi	$2$	$2$	$2^{8} \cdot 3^{2} \cdot 7^{2}$	$2^{15} \cdot 3^{6} \cdot 7^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$3.479426394$	$1$		$3$	$147456$	$1.118288$	$8000$	$0.90298$	$3.23627$	$[0, 0, 0, -5880, -153664]$	$y^2=x^3-5880x-153664$		$[(232, 3312)]$
112896.ci2	112896bi1	112896.ci	112896bi	$2$	$2$	$2^{8} \cdot 3^{2} \cdot 7^{2}$	$2^{9} \cdot 3^{6} \cdot 7^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1.739713197$	$1$		$3$	$73728$	$0.771715$	$8000$	$0.90298$	$2.87880$	$[0, 0, 0, -1470, 19208]$	$y^2=x^3-1470x+19208$		$[(-28, 196)]$
135424.a1	135424k2	135424.a	135424k	$2$	$2$	$2^{8} \cdot 23^{2}$	$2^{15} \cdot 23^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$202752$	$1.163774$	$8000$	$0.90298$	$3.23264$	$[0, 1, 0, -7053, 199531]$	$y^2=x^3+x^2-7053x+199531$		$[]$
135424.a2	135424k1	135424.a	135424k	$2$	$2$	$2^{8} \cdot 23^{2}$	$2^{9} \cdot 23^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$101376$	$0.817201$	$8000$	$0.90298$	$2.88067$	$[0, 1, 0, -1763, -25823]$	$y^2=x^3+x^2-1763x-25823$		$[]$
135424.t1	135424j2	135424.t	135424j	$2$	$2$	$2^{8} \cdot 23^{2}$	$2^{15} \cdot 23^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$8.760920407$	$1$		$1$	$202752$	$1.163774$	$8000$	$0.90298$	$3.23264$	$[0, -1, 0, -7053, -199531]$	$y^2=x^3-x^2-7053x-199531$		$[(-14101/17, 793128/17)]$
135424.t2	135424j1	135424.t	135424j	$2$	$2$	$2^{8} \cdot 23^{2}$	$2^{9} \cdot 23^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$4.380460203$	$1$		$1$	$101376$	$0.817201$	$8000$	$0.90298$	$2.88067$	$[0, -1, 0, -1763, 25823]$	$y^2=x^3-x^2-1763x+25823$		$[(2533/3, 125902/3)]$
215296.c1	215296b2	215296.c	215296b	$2$	$2$	$2^{8} \cdot 29^{2}$	$2^{15} \cdot 29^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$403200$	$1.279675$	$8000$	$0.90298$	$3.22385$	$[0, 1, 0, -11213, 400939]$	$y^2=x^3+x^2-11213x+400939$		$[]$
215296.c2	215296b1	215296.c	215296b	$2$	$2$	$2^{8} \cdot 29^{2}$	$2^{9} \cdot 29^{6}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$201600$	$0.933102$	$8000$	$0.90298$	$2.88518$	$[0, 1, 0, -2803, -51519]$	$y^2=x^3+x^2-2803x-51519$		$[]$
215296.v1	215296w2	215296.v	215296w	$2$	$2$	$2^{8} \cdot 29^{2}$	$2^{15} \cdot 29^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$28.91158430$	$1$		$1$	$403200$	$1.279675$	$8000$	$0.90298$	$3.22385$	$[0, -1, 0, -11213, -400939]$	$y^2=x^3-x^2-11213x-400939$		$[(-2390221562636/217095, 1906444099357961113/217095)]$
215296.v2	215296w1	215296.v	215296w	$2$	$2$	$2^{8} \cdot 29^{2}$	$2^{9} \cdot 29^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$14.45579215$	$1$		$1$	$201600$	$0.933102$	$8000$	$0.90298$	$2.88518$	$[0, -1, 0, -2803, 51519]$	$y^2=x^3-x^2-2803x+51519$		$[(517494/205, 1178685003/205)]$
246016.b1	246016b2	246016.b	246016b	$2$	$2$	$2^{8} \cdot 31^{2}$	$2^{15} \cdot 31^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$4.555391195$	$1$		$3$	$491520$	$1.313021$	$8000$	$0.90298$	$3.22145$	$[0, 1, 0, -12813, -498581]$	$y^2=x^3+x^2-12813x-498581$		$[(205, 2352)]$
246016.b2	246016b1	246016.b	246016b	$2$	$2$	$2^{8} \cdot 31^{2}$	$2^{9} \cdot 31^{6}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓							$2.277695597$	$1$		$1$	$245760$	$0.966448$	$8000$	$0.90298$	$2.88641$	$[0, 1, 0, -3203, 60721]$	$y^2=x^3+x^2-3203x+60721$		$[(-115/2, 2883/2)]$

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