Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
19047851.a1	-	19047851.a	-	$1$	$1$	\( 19047851 \)	\( -19047851 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$14.79052757$	$1$		$78$	$$	$0.108092$	$-54526169088/19047851$	$[0, 0, 1, -79, 342]$	\(y^2+y=x^3-79x+342\)
64921931.a1	-	64921931.a	-	$1$	$1$	\( 64921931 \)	\( -64921931 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20.39878841$	$1$		$70$	$$	$0.234058$	$-533806460928/64921931$	$[0, 0, 1, -169, 930]$	\(y^2+y=x^3-169x+930\)
67445803.a1	-	67445803.a	-	$1$	$1$	\( 67445803 \)	\( -67445803 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$26.51423950$	$1$		$62$	$$	$0.183052$	$-3086626816/67445803$	$[0, 1, 1, -30, 390]$	\(y^2+y=x^3+x^2-30x+390\)
74129723.a1	-	74129723.a	-	$1$	$1$	\( 74129723 \)	\( -74129723 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$22.60191695$	$1$		$66$	$$	$0.295176$	$-3015943483392/74129723$	$[0, 0, 1, -301, 2052]$	\(y^2+y=x^3-301x+2052\)
84602123.a1	-	84602123.a	-	$1$	$1$	\( 84602123 \)	\( -84602123 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20.68192969$	$1$		$72$	$$	$0.349005$	$-10555342073856/84602123$	$[0, 0, 1, -457, 3786]$	\(y^2+y=x^3-457x+3786\)
106974317.a1	-	106974317.a	-	$1$	$1$	\( 106974317 \)	\( 106974317 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$29.35807131$	$1$		$58$	$$	$0.387057$	$21026861362801/106974317$	$[1, 0, 0, -575, 5236]$	\(y^2+xy=x^3-575x+5236\)
111061427.a1	-	111061427.a	-	$1$	$1$	\( 111061427 \)	\( 111061427 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$33.42862426$	$1$		$50$	$$	$0.292223$	$1626794704081/111061427$	$[1, 0, 0, -245, 1366]$	\(y^2+xy=x^3-245x+1366\)
117138251.a1	-	117138251.a	-	$1$	$1$	\( 117138251 \)	\( -117138251 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$36.51205499$	$1$		$50$	$$	$0.238029$	$-61723537408/117138251$	$[0, -1, 1, -82, 622]$	\(y^2+y=x^3-x^2-82x+622\)
122882843.a1	-	122882843.a	-	$1$	$1$	\( 122882843 \)	\( -122882843 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$32.68086475$	$1$		$54$	$$	$0.350086$	$-7095597469696/122882843$	$[0, -1, 1, -400, 3262]$	\(y^2+y=x^3-x^2-400x+3262\)
138437407.a1	-	138437407.a	-	$1$	$1$	\( 138437407 \)	\( 138437407 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$33.01422780$	$1$		$56$	$$	$0.260497$	$349062369921/138437407$	$[1, -1, 1, -147, 420]$	\(y^2+xy+y=x^3-x^2-147x+420\)
161759189.a1	-	161759189.a	-	$1$	$1$	\( 161759189 \)	\( 161759189 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$32.18947765$	$1$		$62$	$$	$0.267619$	$318891962368/161759189$	$[0, 1, 1, -142, 182]$	\(y^2+y=x^3+x^2-142x+182\)
169624549.a1	-	169624549.a	-	$1$	$1$	\( 169624549 \)	\( 169624549 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$35.38965686$	$1$		$60$	$$	$0.268857$	$297007976448/169624549$	$[0, 0, 1, -139, 72]$	\(y^2+y=x^3-139x+72\)
177858971.a1	-	177858971.a	-	$1$	$1$	\( 177858971 \)	\( -177858971 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$25.09168982$	$1$		$68$	$$	$0.429313$	$-34620476018688/177858971$	$[0, 0, 1, -679, 6840]$	\(y^2+y=x^3-679x+6840\)
185220011.a1	-	185220011.a	-	$1$	$1$	\( 185220011 \)	\( -185220011 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$37.53295582$	$1$		$52$	$$	$0.389880$	$-12409821687808/185220011$	$[0, -1, 1, -482, 4290]$	\(y^2+y=x^3-x^2-482x+4290\)
214371643.a1	-	214371643.a	-	$1$	$1$	\( 214371643 \)	\( -214371643 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$33.55718048$	$1$		$64$	$$	$0.288309$	$-111701610496/214371643$	$[0, 1, 1, -100, 770]$	\(y^2+y=x^3+x^2-100x+770\)
232113701.a1	-	232113701.a	-	$1$	$1$	\( 232113701 \)	\( 232113701 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$46.84586516$	$1$		$54$	$$	$0.825884$	$68069240313278464/232113701$	$[0, 1, 1, -8506, 299132]$	\(y^2+y=x^3+x^2-8506x+299132\)
238055563.a1	-	238055563.a	-	$1$	$1$	\( 238055563 \)	\( -238055563 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$38.28603320$	$1$		$52$	$$	$0.328100$	$-1088912207872/238055563$	$[0, 1, 1, -214, 1346]$	\(y^2+y=x^3+x^2-214x+1346\)
271522949.a1	-	271522949.a	-	$1$	$1$	\( 271522949 \)	\( 271522949 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$41.47171113$	$1$		$52$	$$	$0.367385$	$4059246481408/271522949$	$[0, 1, 1, -332, 2082]$	\(y^2+y=x^3+x^2-332x+2082\)
288935749.a1	-	288935749.a	-	$1$	$1$	\( 288935749 \)	\( 288935749 \)	$5$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$30.84778361$	$1$		$70$	$$	$0.347648$	$1921423085568/288935749$	$[0, 0, 1, -259, 1380]$	\(y^2+y=x^3-259x+1380\)