Elliptic curve search results

Results (26 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
3192.j1	3192l1	3192.j	3192l	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 7^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1.585334461$	$1$		$5$	$1152$	$0.171567$	$381775972/25137$	$0.83772$	$3.30819$	$1$	$[0, -1, 0, -152, 732]$	\(y^2=x^3-x^2-152x+732\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-2, 32)]$	$1$
6384.be1	6384l1	6384.be	6384l	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 7^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$0.634954434$	$1$		$9$	$2304$	$0.171567$	$381775972/25137$	$0.83772$	$3.04647$	$1$	$[0, 1, 0, -152, -732]$	\(y^2=x^3+x^2-152x-732\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-8, 6)]$	$1$
9576.b1	9576j1	9576.b	9576j	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 7^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$2.134613423$	$1$		$5$	$9216$	$0.720874$	$381775972/25137$	$0.83772$	$3.63079$	$1$	$[0, 0, 0, -1371, -18394]$	\(y^2=x^3-1371x-18394\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-25, 16)]$	$1$
19152.m1	19152w1	19152.m	19152w	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 7^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$0.526727622$	$1$		$9$	$18432$	$0.720874$	$381775972/25137$	$0.83772$	$3.37555$	$1$	$[0, 0, 0, -1371, 18394]$	\(y^2=x^3-1371x+18394\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(5, 108)]$	$1$
22344.t1	22344be1	22344.t	22344be	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 7^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$55296$	$1.144522$	$381775972/25137$	$0.83772$	$3.83124$	$1$	$[0, 1, 0, -7464, -236160]$	\(y^2=x^3+x^2-7464x-236160\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$	$1$
25536.p1	25536cp1	25536.p	25536cp	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{3} \cdot 7^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$18432$	$0.518141$	$381775972/25137$	$0.83772$	$3.04012$	$1$	$[0, -1, 0, -609, -5247]$	\(y^2=x^3-x^2-609x-5247\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$	$1$
25536.cb1	25536bd1	25536.cb	25536bd	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{3} \cdot 7^{2} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$0.912851274$	$1$		$19$	$18432$	$0.518141$	$381775972/25137$	$0.83772$	$3.04012$	$1$	$[0, 1, 0, -609, 5247]$	\(y^2=x^3+x^2-609x+5247\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(27, 96), (18, 21)]$	$1$
44688.d1	44688o1	44688.d	44688o	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 7^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1.207193479$	$1$		$7$	$110592$	$1.144522$	$381775972/25137$	$0.83772$	$3.58323$	$1$	$[0, -1, 0, -7464, 236160]$	\(y^2=x^3-x^2-7464x+236160\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(68, 196)]$	$1$
60648.bo1	60648p1	60648.bo	60648p	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{3} \cdot 7^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$5.066781169$	$1$		$3$	$414720$	$1.643787$	$381775972/25137$	$0.83772$	$4.02788$	$1$	$[0, 1, 0, -54992, -4691088]$	\(y^2=x^3+x^2-54992x-4691088\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(739, 18942)]$	$1$
67032.cb1	67032x1	67032.cb	67032x	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 7^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1.797086242$	$1$		$3$	$442368$	$1.693829$	$381775972/25137$	$0.83772$	$4.04564$	$1$	$[0, 0, 0, -67179, 6309142]$	\(y^2=x^3-67179x+6309142\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(791, 21168)]$	$1$
76608.ep1	76608bd1	76608.ep	76608bd	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{9} \cdot 7^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$147456$	$1.067448$	$381775972/25137$	$0.83772$	$3.32926$	$1$	$[0, 0, 0, -5484, -147152]$	\(y^2=x^3-5484x-147152\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$	$1$
76608.es1	76608fo1	76608.es	76608fo	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{9} \cdot 7^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$2.315742180$	$1$		$5$	$147456$	$1.067448$	$381775972/25137$	$0.83772$	$3.32926$	$1$	$[0, 0, 0, -5484, 147152]$	\(y^2=x^3-5484x+147152\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(16, 252)]$	$1$
79800.bx1	79800p1	79800.bx	79800p	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{6} \cdot 7^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$147456$	$0.976286$	$381775972/25137$	$0.83772$	$3.22030$	$1$	$[0, 1, 0, -3808, 83888]$	\(y^2=x^3+x^2-3808x+83888\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$	$1$
121296.bn1	121296t1	121296.bn	121296t	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{3} \cdot 7^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1.572319234$	$1$		$3$	$829440$	$1.643787$	$381775972/25137$	$0.83772$	$3.78938$	$1$	$[0, -1, 0, -54992, 4691088]$	\(y^2=x^3-x^2-54992x+4691088\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-234, 2166)]$	$1$
134064.fh1	134064fc1	134064.fh	134064fc	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 7^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$884736$	$1.693829$	$381775972/25137$	$0.83772$	$3.80812$	$1$	$[0, 0, 0, -67179, -6309142]$	\(y^2=x^3-67179x-6309142\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$	$1$
159600.c1	159600gq1	159600.c	159600gq	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{6} \cdot 7^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$2.022059112$	$1$		$7$	$294912$	$0.976286$	$381775972/25137$	$0.83772$	$3.03399$	$1$	$[0, -1, 0, -3808, -83888]$	\(y^2=x^3-x^2-3808x-83888\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-42, 14)]$	$1$
178752.dw1	178752kb1	178752.dw	178752kb	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{3} \cdot 7^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$4.305506770$	$1$		$3$	$884736$	$1.491096$	$381775972/25137$	$0.83772$	$3.51637$	$1$	$[0, -1, 0, -29857, -1859423]$	\(y^2=x^3-x^2-29857x-1859423\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(321, 4640)]$	$1$
178752.jx1	178752co1	178752.jx	178752co	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{3} \cdot 7^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$884736$	$1.491096$	$381775972/25137$	$0.83772$	$3.51637$	$1$	$[0, 1, 0, -29857, 1859423]$	\(y^2=x^3+x^2-29857x+1859423\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$	$1$
181944.b1	181944a1	181944.b	181944a	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{9} \cdot 7^{2} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$3317760$	$2.193092$	$381775972/25137$	$0.83772$	$4.20677$	$1$	$[0, 0, 0, -494931, 126164446]$	\(y^2=x^3-494931x+126164446\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$	$1$
239400.cj1	239400cj1	239400.cj	239400cj	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 5^{6} \cdot 7^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1.859040829$	$1$		$5$	$1179648$	$1.525593$	$381775972/25137$	$0.83772$	$3.46686$	$1$	$[0, 0, 0, -34275, -2299250]$	\(y^2=x^3-34275x-2299250\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-106, 378)]$	$1$
363888.bb1	363888bb1	363888.bb	363888bb	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{9} \cdot 7^{2} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$6635520$	$2.193092$	$381775972/25137$	$0.83772$	$3.97905$	$1$	$[0, 0, 0, -494931, -126164446]$	\(y^2=x^3-494931x-126164446\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$	$1$
386232.ba1	386232ba1	386232.ba	386232ba	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 7^{2} \cdot 11^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$11.24964541$	$1$		$1$	$1244160$	$1.370516$	$381775972/25137$	$0.83772$	$3.19330$	$1$	$[0, -1, 0, -18432, -900612]$	\(y^2=x^3-x^2-18432x-900612\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-178934/51, 25547696/51)]$	$1$
424536.o1	424536o1	424536.o	424536o	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( 2^{10} \cdot 3^{3} \cdot 7^{8} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$4.443823191$	$1$		$1$	$19906560$	$2.616741$	$381775972/25137$	$0.83772$	$4.32402$	$1$	$[0, -1, 0, -2694624, 1603653948]$	\(y^2=x^3-x^2-2694624x+1603653948\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(6178/3, 236816/3)]$	$1$
478800.hr1	478800hr1	478800.hr	478800hr	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 5^{6} \cdot 7^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$2359296$	$1.525593$	$381775972/25137$	$0.83772$	$3.28313$	$1$	$[0, 0, 0, -34275, 2299250]$	\(y^2=x^3-34275x+2299250\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$	$1$
485184.m1	485184m1	485184.m	485184m	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{16} \cdot 3^{3} \cdot 7^{2} \cdot 19^{7} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$4.436814053$	$1$		$13$	$6635520$	$1.990360$	$381775972/25137$	$0.83772$	$3.70580$	$1$	$[0, -1, 0, -219969, -37308735]$	\(y^2=x^3-x^2-219969x-37308735\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-253, 1444), (5665/3, 231040/3)]$	$1$
485184.fv1	485184fv1	485184.fv	485184fv	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{16} \cdot 3^{3} \cdot 7^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$2.298081643$	$1$		$5$	$6635520$	$1.990360$	$381775972/25137$	$0.83772$	$3.70580$	$1$	$[0, 1, 0, -219969, 37308735]$	\(y^2=x^3+x^2-219969x+37308735\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(327, 672)]$	$1$

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