Elliptic curve search results

Results (31 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
498.a1	498b1	498.a	498b	$1$	$1$	\( 2 \cdot 3 \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$996$	$2$	$0$	$0.059248216$	$1$		$12$	$80$	$-0.258325$	$-68417929/322704$	$0.90619$	$3.26135$	$[1, 0, 1, -9, 28]$	\(y^2+xy+y=x^3-9x+28\)	996.2.0.?	$[(-1, 6)]$
1494.d1	1494c1	1494.d	1494c	$1$	$1$	\( 2 \cdot 3^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{11} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$0.318828539$	$1$		$6$	$640$	$0.290981$	$-68417929/322704$	$0.90619$	$3.67298$	$[1, -1, 1, -77, -763]$	\(y^2+xy+y=x^3-x^2-77x-763\)	996.2.0.?	$[(21, 70)]$
3984.d1	3984b1	3984.d	3984b	$1$	$1$	\( 2^{4} \cdot 3 \cdot 83 \)	\( - 2^{16} \cdot 3^{5} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$1920$	$0.434823$	$-68417929/322704$	$0.90619$	$3.44663$	$[0, -1, 0, -136, -1808]$	\(y^2=x^3-x^2-136x-1808\)	996.2.0.?	$[ ]$
11952.k1	11952s1	11952.k	11952s	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 83 \)	\( - 2^{16} \cdot 3^{11} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$15360$	$0.984129$	$-68417929/322704$	$0.90619$	$3.74541$	$[0, 0, 0, -1227, 50042]$	\(y^2=x^3-1227x+50042\)	996.2.0.?	$[ ]$
12450.u1	12450m1	12450.u	12450m	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 5^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$11200$	$0.546394$	$-68417929/322704$	$0.90619$	$3.17213$	$[1, 1, 1, -213, 3531]$	\(y^2+xy+y=x^3+x^2-213x+3531\)	996.2.0.?	$[ ]$
15936.f1	15936a1	15936.f	15936a	$1$	$1$	\( 2^{6} \cdot 3 \cdot 83 \)	\( - 2^{22} \cdot 3^{5} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$0.962943007$	$1$		$4$	$15360$	$0.781396$	$-68417929/322704$	$0.90619$	$3.38264$	$[0, -1, 0, -545, 15009]$	\(y^2=x^3-x^2-545x+15009\)	996.2.0.?	$[(25, 128)]$
15936.v1	15936w1	15936.v	15936w	$1$	$1$	\( 2^{6} \cdot 3 \cdot 83 \)	\( - 2^{22} \cdot 3^{5} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$15360$	$0.781396$	$-68417929/322704$	$0.90619$	$3.38264$	$[0, 1, 0, -545, -15009]$	\(y^2=x^3+x^2-545x-15009\)	996.2.0.?	$[ ]$
24402.d1	24402a1	24402.d	24402a	$1$	$1$	\( 2 \cdot 3 \cdot 7^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 7^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$23040$	$0.714630$	$-68417929/322704$	$0.90619$	$3.16067$	$[1, 1, 0, -417, -10107]$	\(y^2+xy=x^3+x^2-417x-10107\)	996.2.0.?	$[ ]$
37350.ba1	37350t1	37350.ba	37350t	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{11} \cdot 5^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$3.731169378$	$1$		$2$	$89600$	$1.095701$	$-68417929/322704$	$0.90619$	$3.46722$	$[1, -1, 0, -1917, -97259]$	\(y^2+xy=x^3-x^2-1917x-97259\)	996.2.0.?	$[(218, 3023)]$
41334.k1	41334h1	41334.k	41334h	$1$	$1$	\( 2 \cdot 3 \cdot 83^{2} \)	\( - 2^{4} \cdot 3^{5} \cdot 83^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$551040$	$1.951096$	$-68417929/322704$	$0.90619$	$4.39985$	$[1, 0, 0, -58700, -16563552]$	\(y^2+xy=x^3-58700x-16563552\)	996.2.0.?	$[ ]$
47808.z1	47808w1	47808.z	47808w	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 83 \)	\( - 2^{22} \cdot 3^{11} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$2.687221279$	$1$		$2$	$122880$	$1.330702$	$-68417929/322704$	$0.90619$	$3.64951$	$[0, 0, 0, -4908, -400336]$	\(y^2=x^3-4908x-400336\)	996.2.0.?	$[(182, 2176)]$
47808.bg1	47808bm1	47808.bg	47808bm	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 83 \)	\( - 2^{22} \cdot 3^{11} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1.596669821$	$1$		$2$	$122880$	$1.330702$	$-68417929/322704$	$0.90619$	$3.64951$	$[0, 0, 0, -4908, 400336]$	\(y^2=x^3-4908x+400336\)	996.2.0.?	$[(-4, 648)]$
60258.ba1	60258z1	60258.ba	60258z	$1$	$1$	\( 2 \cdot 3 \cdot 11^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 11^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$108000$	$0.940623$	$-68417929/322704$	$0.90619$	$3.14747$	$[1, 0, 0, -1031, -38631]$	\(y^2+xy=x^3-1031x-38631\)	996.2.0.?	$[ ]$
73206.bh1	73206bq1	73206.bh	73206bq	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{11} \cdot 7^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1.011658108$	$1$		$4$	$184320$	$1.263937$	$-68417929/322704$	$0.90619$	$3.43915$	$[1, -1, 1, -3758, 269133]$	\(y^2+xy+y=x^3-x^2-3758x+269133\)	996.2.0.?	$[(23, 429)]$
84162.z1	84162t1	84162.z	84162t	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 13^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$0.531773343$	$1$		$4$	$153600$	$1.024151$	$-68417929/322704$	$0.90619$	$3.14313$	$[1, 0, 0, -1440, 63504]$	\(y^2+xy=x^3-1440x+63504\)	996.2.0.?	$[(66, 474)]$
99600.bv1	99600db1	99600.bv	99600db	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 83 \)	\( - 2^{16} \cdot 3^{5} \cdot 5^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$268800$	$1.239542$	$-68417929/322704$	$0.90619$	$3.32171$	$[0, 1, 0, -3408, -232812]$	\(y^2=x^3+x^2-3408x-232812\)	996.2.0.?	$[ ]$
124002.d1	124002g1	124002.d	124002g	$1$	$1$	\( 2 \cdot 3^{2} \cdot 83^{2} \)	\( - 2^{4} \cdot 3^{11} \cdot 83^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$0.688044528$	$1$		$4$	$4408320$	$2.500401$	$-68417929/322704$	$0.90619$	$4.54975$	$[1, -1, 0, -528300, 447215904]$	\(y^2+xy=x^3-x^2-528300x+447215904\)	996.2.0.?	$[(1017, 30492)]$
143922.g1	143922bc1	143922.g	143922bc	$1$	$1$	\( 2 \cdot 3 \cdot 17^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 17^{6} \cdot 83 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$3.601375162$	$1$		$8$	$394240$	$1.158281$	$-68417929/322704$	$0.90619$	$3.13666$	$[1, 1, 0, -2462, 141252]$	\(y^2+xy=x^3+x^2-2462x+141252\)	996.2.0.?	$[(-33, 450), (256, 3918)]$
179778.i1	179778c1	179778.i	179778c	$1$	$1$	\( 2 \cdot 3 \cdot 19^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 19^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$563040$	$1.213894$	$-68417929/322704$	$0.90619$	$3.13415$	$[1, 1, 1, -3076, -199915]$	\(y^2+xy+y=x^3+x^2-3076x-199915\)	996.2.0.?	$[ ]$
180774.n1	180774bg1	180774.n	180774bg	$1$	$1$	\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{11} \cdot 11^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$864000$	$1.489929$	$-68417929/322704$	$0.90619$	$3.40636$	$[1, -1, 0, -9279, 1043037]$	\(y^2+xy=x^3-x^2-9279x+1043037\)	996.2.0.?	$[ ]$
195216.cq1	195216t1	195216.cq	195216t	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 83 \)	\( - 2^{16} \cdot 3^{5} \cdot 7^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1.106541107$	$1$		$4$	$552960$	$1.407778$	$-68417929/322704$	$0.90619$	$3.30394$	$[0, 1, 0, -6680, 633492]$	\(y^2=x^3+x^2-6680x+633492\)	996.2.0.?	$[(-68, 882)]$
252486.o1	252486o1	252486.o	252486o	$1$	$1$	\( 2 \cdot 3^{2} \cdot 13^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{11} \cdot 13^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$2.212027949$	$1$		$2$	$1228800$	$1.573456$	$-68417929/322704$	$0.90619$	$3.39544$	$[1, -1, 0, -12960, -1714608]$	\(y^2+xy=x^3-x^2-12960x-1714608\)	996.2.0.?	$[(1323, 47250)]$
263442.o1	263442o1	263442.o	263442o	$1$	$1$	\( 2 \cdot 3 \cdot 23^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 23^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$3.405044069$	$1$		$2$	$1012000$	$1.309422$	$-68417929/322704$	$0.90619$	$3.13004$	$[1, 0, 1, -4508, -352726]$	\(y^2+xy+y=x^3-4508x-352726\)	996.2.0.?	$[(93, 139)]$
298800.n1	298800n1	298800.n	298800n	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 83 \)	\( - 2^{16} \cdot 3^{11} \cdot 5^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$2.459745160$	$1$		$2$	$2150400$	$1.788847$	$-68417929/322704$	$0.90619$	$3.55510$	$[0, 0, 0, -30675, 6255250]$	\(y^2=x^3-30675x+6255250\)	996.2.0.?	$[(71, 2106)]$
330672.f1	330672f1	330672.f	330672f	$1$	$1$	\( 2^{4} \cdot 3 \cdot 83^{2} \)	\( - 2^{16} \cdot 3^{5} \cdot 83^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$7.964606677$	$1$		$0$	$13224960$	$2.644241$	$-68417929/322704$	$0.90619$	$4.33443$	$[0, -1, 0, -939200, 1060067328]$	\(y^2=x^3-x^2-939200x+1060067328\)	996.2.0.?	$[(574473/16, 414642021/16)]$
398400.k1	398400k1	398400.k	398400k	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 83 \)	\( - 2^{22} \cdot 3^{5} \cdot 5^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$2150400$	$1.586115$	$-68417929/322704$	$0.90619$	$3.28713$	$[0, -1, 0, -13633, -1848863]$	\(y^2=x^3-x^2-13633x-1848863\)	996.2.0.?	$[ ]$
398400.ix1	398400ix1	398400.ix	398400ix	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 83 \)	\( - 2^{22} \cdot 3^{5} \cdot 5^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1.387729552$	$1$		$4$	$2150400$	$1.586115$	$-68417929/322704$	$0.90619$	$3.28713$	$[0, 1, 0, -13633, 1848863]$	\(y^2=x^3+x^2-13633x+1848863\)	996.2.0.?	$[(-133, 1152)]$
418818.k1	418818k1	418818.k	418818k	$1$	$1$	\( 2 \cdot 3 \cdot 29^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 29^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1.244452727$	$1$		$4$	$1980160$	$1.425323$	$-68417929/322704$	$0.90619$	$3.12539$	$[1, 1, 1, -7166, 703307]$	\(y^2+xy+y=x^3+x^2-7166x+703307\)	996.2.0.?	$[(-85, 883)]$
431766.bp1	431766bp1	431766.bp	431766bp	$1$	$1$	\( 2 \cdot 3^{2} \cdot 17^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{11} \cdot 17^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$5.125215936$	$1$		$0$	$3153920$	$1.707588$	$-68417929/322704$	$0.90619$	$3.37909$	$[1, -1, 1, -22163, -3835965]$	\(y^2+xy+y=x^3-x^2-22163x-3835965\)	996.2.0.?	$[(2415/2, 111447/2)]$
478578.d1	478578d1	478578.d	478578d	$1$	$1$	\( 2 \cdot 3 \cdot 31^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{5} \cdot 31^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$2448000$	$1.458670$	$-68417929/322704$	$0.90619$	$3.12411$	$[1, 1, 0, -8188, -866144]$	\(y^2+xy=x^3+x^2-8188x-866144\)	996.2.0.?	$[ ]$
482064.o1	482064o1	482064.o	482064o	$1$	$1$	\( 2^{4} \cdot 3 \cdot 11^{2} \cdot 83 \)	\( - 2^{16} \cdot 3^{5} \cdot 11^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$996$	$2$	$0$	$1$	$1$		$0$	$2592000$	$1.633770$	$-68417929/322704$	$0.90619$	$3.28295$	$[0, -1, 0, -16496, 2472384]$	\(y^2=x^3-x^2-16496x+2472384\)	996.2.0.?	$[ ]$

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