Elliptic curve search results

Results (19 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
19047851.a1	-	19047851.a	-	$1$	$1$	\( 19047851 \)	\( -19047851 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$38095702$	$2$	$0$	$14.79052757$	$1$		$78$		$0.108092$	$-54526169088/19047851$	$0.66854$	$1.50301$	$[0, 0, 1, -79, 342]$	\(y^2+y=x^3-79x+342\)	38095702.2.0.?	$[(3, 11), (7, 11), (10, 23), (-6, 24), (4, 9)]$
64921931.a1	-	64921931.a	-	$1$	$1$	\( 64921931 \)	\( -64921931 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$129843862$	$2$	$0$	$20.39878841$	$1$		$70$		$0.234058$	$-533806460928/64921931$	$0.74611$	$1.51173$	$[0, 0, 1, -169, 930]$	\(y^2+y=x^3-169x+930\)	129843862.2.0.?	$[(8, 9), (7, 9), (6, 11), (0, 30), (20, 74)]$
67445803.a1	-	67445803.a	-	$1$	$1$	\( 67445803 \)	\( -67445803 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$134891606$	$2$	$0$	$26.51423950$	$1$		$62$		$0.183052$	$-3086626816/67445803$	$0.60990$	$1.41498$	$[0, 1, 1, -30, 390]$	\(y^2+y=x^3+x^2-30x+390\)	134891606.2.0.?	$[(2, 18), (-9, 3), (-7, 17), (-4, 21), (15, 59)]$
74129723.a1	-	74129723.a	-	$1$	$1$	\( 74129723 \)	\( -74129723 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$148259446$	$2$	$0$	$22.60191695$	$1$		$66$		$0.295176$	$-3015943483392/74129723$	$0.61565$	$1.58799$	$[0, 0, 1, -301, 2052]$	\(y^2+y=x^3-301x+2052\)	148259446.2.0.?	$[(10, 6), (9, 8), (8, 12), (11, 8), (19, 56)]$
84602123.a1	-	84602123.a	-	$1$	$1$	\( 84602123 \)	\( -84602123 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$169204246$	$2$	$0$	$20.68192969$	$1$		$72$		$0.349005$	$-10555342073856/84602123$	$0.62988$	$1.64360$	$[0, 0, 1, -457, 3786]$	\(y^2+y=x^3-457x+3786\)	169204246.2.0.?	$[(11, 9), (14, 11), (15, 17), (12, 5), (13, 6)]$
106974317.a1	-	106974317.a	-	$1$	$1$	\( 106974317 \)	\( 106974317 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$213948634$	$2$	$0$	$29.35807131$	$1$		$58$		$0.387057$	$21026861362801/106974317$	$0.66922$	$1.65927$	$[1, 0, 0, -575, 5236]$	\(y^2+xy=x^3-575x+5236\)	213948634.2.0.?	$[(13, -6), (15, -1), (12, 4), (16, 6), (11, 11)]$
111061427.a1	-	111061427.a	-	$1$	$1$	\( 111061427 \)	\( 111061427 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$444245708$	$2$	$0$	$33.42862426$	$1$		$50$		$0.292223$	$1626794704081/111061427$	$0.64363$	$1.51777$	$[1, 0, 0, -245, 1366]$	\(y^2+xy=x^3-245x+1366\)	444245708.2.0.?	$[(6, 8), (5, 14), (7, -6), (15, 26), (13, 14)]$
117138251.a1	-	117138251.a	-	$1$	$1$	\( 117138251 \)	\( -117138251 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$234276502$	$2$	$0$	$36.51205499$	$1$		$50$		$0.238029$	$-61723537408/117138251$	$0.59920$	$1.41557$	$[0, -1, 1, -82, 622]$	\(y^2+y=x^3-x^2-82x+622\)	234276502.2.0.?	$[(4, 18), (7, 18), (-4, 29), (11, 30), (2, 21)]$
122882843.a1	-	122882843.a	-	$1$	$1$	\( 122882843 \)	\( -122882843 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$245765686$	$2$	$0$	$32.68086475$	$1$		$54$		$0.350086$	$-7095597469696/122882843$	$0.63273$	$1.59019$	$[0, -1, 1, -400, 3262]$	\(y^2+y=x^3-x^2-400x+3262\)	245765686.2.0.?	$[(11, 8), (13, 9), (14, 14), (7, 27), (20, 53)]$
138437407.a1	-	138437407.a	-	$1$	$1$	\( 138437407 \)	\( 138437407 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$553749628$	$2$	$0$	$33.01422780$	$1$		$56$		$0.260497$	$349062369921/138437407$	$0.64487$	$1.41783$	$[1, -1, 1, -147, 420]$	\(y^2+xy+y=x^3-x^2-147x+420\)	553749628.2.0.?	$[(2, 10), (11, 1), (0, 20), (-6, 35), (3, -3)]$
161759189.a1	-	161759189.a	-	$1$	$1$	\( 161759189 \)	\( 161759189 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$323518378$	$2$	$0$	$32.18947765$	$1$		$62$		$0.267619$	$318891962368/161759189$	$0.60564$	$1.40137$	$[0, 1, 1, -142, 182]$	\(y^2+y=x^3+x^2-142x+182\)	323518378.2.0.?	$[(0, 13), (11, 8), (-2, 21), (1, 6), (13, 26)]$
169624549.a1	-	169624549.a	-	$1$	$1$	\( 169624549 \)	\( 169624549 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$339249098$	$2$	$0$	$35.38965686$	$1$		$60$		$0.268857$	$297007976448/169624549$	$0.66514$	$1.39410$	$[0, 0, 1, -139, 72]$	\(y^2+y=x^3-139x+72\)	339249098.2.0.?	$[(-1, 14), (-7, 26), (0, 8), (-2, 18), (-12, 3)]$
177858971.a1	-	177858971.a	-	$1$	$1$	\( 177858971 \)	\( -177858971 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$355717942$	$2$	$0$	$25.09168982$	$1$		$68$		$0.429313$	$-34620476018688/177858971$	$0.63235$	$1.64158$	$[0, 0, 1, -679, 6840]$	\(y^2+y=x^3-679x+6840\)	355717942.2.0.?	$[(16, 8), (11, 26), (13, 14), (17, 14), (15, 5)]$
185220011.a1	-	185220011.a	-	$1$	$1$	\( 185220011 \)	\( -185220011 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$370440022$	$2$	$0$	$37.53295582$	$1$		$52$		$0.389880$	$-12409821687808/185220011$	$0.63278$	$1.58507$	$[0, -1, 1, -482, 4290]$	\(y^2+y=x^3-x^2-482x+4290\)	370440022.2.0.?	$[(12, 9), (9, 24), (14, 9), (15, 14), (3, 53)]$
214371643.a1	-	214371643.a	-	$1$	$1$	\( 214371643 \)	\( -214371643 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$428743286$	$2$	$0$	$33.55718048$	$1$		$64$		$0.288309$	$-111701610496/214371643$	$0.59765$	$1.40234$	$[0, 1, 1, -100, 770]$	\(y^2+y=x^3+x^2-100x+770\)	428743286.2.0.?	$[(7, 21), (-1, 29), (11, 33), (22, 98), (-4, 33)]$
232113701.a1	-	232113701.a	-	$1$	$1$	\( 232113701 \)	\( 232113701 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$464227402$	$2$	$0$	$46.84586516$	$1$		$54$		$0.825884$	$68069240313278464/232113701$	$0.75322$	$2.01214$	$[0, 1, 1, -8506, 299132]$	\(y^2+y=x^3+x^2-8506x+299132\)	464227402.2.0.?	$[(53, 0), (52, 11), (55, 26), (50, 36), (33, 235)]$
238055563.a1	-	238055563.a	-	$1$	$1$	\( 238055563 \)	\( -238055563 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$476111126$	$2$	$0$	$38.28603320$	$1$		$52$		$0.328100$	$-1088912207872/238055563$	$0.60473$	$1.45358$	$[0, 1, 1, -214, 1346]$	\(y^2+y=x^3+x^2-214x+1346\)	476111126.2.0.?	$[(10, 17), (-1, 39), (2, 30), (12, 25), (8, 14)]$
271522949.a1	-	271522949.a	-	$1$	$1$	\( 271522949 \)	\( 271522949 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$543045898$	$2$	$0$	$41.47171113$	$1$		$52$		$0.367385$	$4059246481408/271522949$	$0.61428$	$1.49499$	$[0, 1, 1, -332, 2082]$	\(y^2+y=x^3+x^2-332x+2082\)	543045898.2.0.?	$[(13, 11), (6, 18), (3, 33), (8, 1), (17, 40)]$
288935749.a1	-	288935749.a	-	$1$	$1$	\( 288935749 \)	\( 288935749 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$577871498$	$2$	$0$	$30.84778361$	$1$		$70$		$0.347648$	$1921423085568/288935749$	$0.58763$	$1.45183$	$[0, 0, 1, -259, 1380]$	\(y^2+y=x^3-259x+1380\)	577871498.2.0.?	$[(15, 29), (16, 36), (2, 29), (6, 6), (1, 33)]$