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	Manin constant
645.e1	645b1	645.e	645b	$2$	$2$	\( 3 \cdot 5 \cdot 43 \)	\( 3^{3} \cdot 5^{2} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$72$	$-0.357348$	$1263214441/29025$	$0.85169$	$3.23947$	$[1, 1, 0, -22, 31]$	\(y^2+xy=x^3+x^2-22x+31\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
1935.d1	1935f1	1935.d	1935f	$2$	$2$	\( 3^{2} \cdot 5 \cdot 43 \)	\( 3^{9} \cdot 5^{2} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$576$	$0.191958$	$1263214441/29025$	$0.85169$	$3.64021$	$[1, -1, 1, -203, -1038]$	\(y^2+xy+y=x^3-x^2-203x-1038\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
3225.c1	3225g1	3225.c	3225g	$2$	$2$	\( 3 \cdot 5^{2} \cdot 43 \)	\( 3^{3} \cdot 5^{8} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$0.454194674$	$1$		$7$	$1728$	$0.447371$	$1263214441/29025$	$0.85169$	$3.78942$	$[1, 0, 0, -563, 4992]$	\(y^2+xy=x^3-563x+4992\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(7, 34)]$	$1$
9675.q1	9675o1	9675.q	9675o	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 43 \)	\( 3^{9} \cdot 5^{8} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.967971475$	$1$		$3$	$13824$	$0.996677$	$1263214441/29025$	$0.85169$	$4.05405$	$[1, -1, 0, -5067, -134784]$	\(y^2+xy=x^3-x^2-5067x-134784\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(204, 2598)]$	$1$
10320.be1	10320bj1	10320.be	10320bj	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$0.796141114$	$1$		$7$	$4608$	$0.335799$	$1263214441/29025$	$0.85169$	$3.16763$	$[0, 1, 0, -360, -2700]$	\(y^2=x^3+x^2-360x-2700\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(-12, 6)]$	$1$
27735.c1	27735i1	27735.c	27735i	$2$	$2$	\( 3 \cdot 5 \cdot 43^{2} \)	\( 3^{3} \cdot 5^{2} \cdot 43^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.290931459$	$1$		$3$	$133056$	$1.523252$	$1263214441/29025$	$0.85169$	$4.25437$	$[1, 0, 0, -41641, -3208504]$	\(y^2+xy=x^3-41641x-3208504\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(283, 2632)]$	$1$
30960.a1	30960br1	30960.a	30960br	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 43 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$0.852331492$	$1$		$23$	$36864$	$0.885105$	$1263214441/29025$	$0.85169$	$3.46855$	$[0, 0, 0, -3243, 69658]$	\(y^2=x^3-3243x+69658\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(53, 216), (26, 54)]$	$1$
31605.x1	31605r1	31605.x	31605r	$2$	$2$	\( 3 \cdot 5 \cdot 7^{2} \cdot 43 \)	\( 3^{3} \cdot 5^{2} \cdot 7^{6} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.610917699$	$1$		$3$	$20736$	$0.615607$	$1263214441/29025$	$0.85169$	$3.14952$	$[1, 0, 1, -1104, -13919]$	\(y^2+xy+y=x^3-1104x-13919\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(179, 2262)]$	$1$
41280.a1	41280cb1	41280.a	41280cb	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{18} \cdot 3^{3} \cdot 5^{2} \cdot 43 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$4.253364268$	$1$		$11$	$36864$	$0.682373$	$1263214441/29025$	$0.85169$	$3.14576$	$[0, -1, 0, -1441, -20159]$	\(y^2=x^3-x^2-1441x-20159\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(-24, 5), (-21, 20)]$	$1$
41280.cq1	41280bh1	41280.cq	41280bh	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{18} \cdot 3^{3} \cdot 5^{2} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$0.996163549$	$1$		$5$	$36864$	$0.682373$	$1263214441/29025$	$0.85169$	$3.14576$	$[0, 1, 0, -1441, 20159]$	\(y^2=x^3+x^2-1441x+20159\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(29, 60)]$	$1$
51600.by1	51600bv1	51600.by	51600bv	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( 2^{12} \cdot 3^{3} \cdot 5^{8} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$110592$	$1.140518$	$1263214441/29025$	$0.85169$	$3.58772$	$[0, -1, 0, -9008, -319488]$	\(y^2=x^3-x^2-9008x-319488\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
78045.d1	78045j1	78045.d	78045j	$2$	$2$	\( 3 \cdot 5 \cdot 11^{2} \cdot 43 \)	\( 3^{3} \cdot 5^{2} \cdot 11^{6} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$100800$	$0.841599$	$1263214441/29025$	$0.85169$	$3.13752$	$[1, 1, 1, -2725, -54790]$	\(y^2+xy+y=x^3+x^2-2725x-54790\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
83205.r1	83205t1	83205.r	83205t	$2$	$2$	\( 3^{2} \cdot 5 \cdot 43^{2} \)	\( 3^{9} \cdot 5^{2} \cdot 43^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$1064448$	$2.072559$	$1263214441/29025$	$0.85169$	$4.42365$	$[1, -1, 0, -374769, 86629608]$	\(y^2+xy=x^3-x^2-374769x+86629608\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
94815.m1	94815bg1	94815.m	94815bg	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 43 \)	\( 3^{9} \cdot 5^{2} \cdot 7^{6} \cdot 43 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.470670776$	$1$		$15$	$165888$	$1.164913$	$1263214441/29025$	$0.85169$	$3.42279$	$[1, -1, 1, -9932, 375806]$	\(y^2+xy+y=x^3-x^2-9932x+375806\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(66, 34), (39, 196)]$	$1$
109005.b1	109005a1	109005.b	109005a	$2$	$2$	\( 3 \cdot 5 \cdot 13^{2} \cdot 43 \)	\( 3^{3} \cdot 5^{2} \cdot 13^{6} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.039637894$	$1$		$7$	$165888$	$0.925126$	$1263214441/29025$	$0.85169$	$3.13356$	$[1, 1, 1, -3806, 86978]$	\(y^2+xy+y=x^3+x^2-3806x+86978\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(44, 62)]$	$1$
123840.dy1	123840gd1	123840.dy	123840gd	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( 2^{18} \cdot 3^{9} \cdot 5^{2} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$294912$	$1.231678$	$1263214441/29025$	$0.85169$	$3.41316$	$[0, 0, 0, -12972, 557264]$	\(y^2=x^3-12972x+557264\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
123840.gf1	123840di1	123840.gf	123840di	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( 2^{18} \cdot 3^{9} \cdot 5^{2} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$294912$	$1.231678$	$1263214441/29025$	$0.85169$	$3.41316$	$[0, 0, 0, -12972, -557264]$	\(y^2=x^3-12972x-557264\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
138675.r1	138675v1	138675.r	138675v	$2$	$2$	\( 3 \cdot 5^{2} \cdot 43^{2} \)	\( 3^{3} \cdot 5^{8} \cdot 43^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$3193344$	$2.327972$	$1263214441/29025$	$0.85169$	$4.49166$	$[1, 1, 0, -1041025, -401063000]$	\(y^2+xy=x^3+x^2-1041025x-401063000\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
154800.fv1	154800dh1	154800.fv	154800dh	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 43 \)	\( 2^{12} \cdot 3^{9} \cdot 5^{8} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.962095190$	$1$		$7$	$884736$	$1.689825$	$1263214441/29025$	$0.85169$	$3.80949$	$[0, 0, 0, -81075, 8707250]$	\(y^2=x^3-81075x+8707250\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(185, 200)]$	$1$
158025.f1	158025m1	158025.f	158025m	$2$	$2$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 43 \)	\( 3^{3} \cdot 5^{8} \cdot 7^{6} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$4.167601078$	$1$		$3$	$497664$	$1.420326$	$1263214441/29025$	$0.85169$	$3.53277$	$[1, 1, 1, -27588, -1739844]$	\(y^2+xy+y=x^3+x^2-27588x-1739844\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(356, 5628)]$	$1$
186405.g1	186405h1	186405.g	186405h	$2$	$2$	\( 3 \cdot 5 \cdot 17^{2} \cdot 43 \)	\( 3^{3} \cdot 5^{2} \cdot 17^{6} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$373248$	$1.059259$	$1263214441/29025$	$0.85169$	$3.12765$	$[1, 0, 1, -6509, 197507]$	\(y^2+xy+y=x^3-6509x+197507\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
206400.l1	206400iz1	206400.l	206400iz	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( 2^{18} \cdot 3^{3} \cdot 5^{8} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.834606011$	$1$		$5$	$884736$	$1.487091$	$1263214441/29025$	$0.85169$	$3.52114$	$[0, -1, 0, -36033, 2591937]$	\(y^2=x^3-x^2-36033x+2591937\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(47, 1000)]$	$1$
206400.kg1	206400cl1	206400.kg	206400cl	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( 2^{18} \cdot 3^{3} \cdot 5^{8} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$884736$	$1.487091$	$1263214441/29025$	$0.85169$	$3.52114$	$[0, 1, 0, -36033, -2591937]$	\(y^2=x^3+x^2-36033x-2591937\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
232845.h1	232845h1	232845.h	232845h	$2$	$2$	\( 3 \cdot 5 \cdot 19^{2} \cdot 43 \)	\( 3^{3} \cdot 5^{2} \cdot 19^{6} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$471744$	$1.114872$	$1263214441/29025$	$0.85169$	$3.12536$	$[1, 0, 0, -8130, -277173]$	\(y^2+xy=x^3-8130x-277173\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
234135.y1	234135y1	234135.y	234135y	$2$	$2$	\( 3^{2} \cdot 5 \cdot 11^{2} \cdot 43 \)	\( 3^{9} \cdot 5^{2} \cdot 11^{6} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$806400$	$1.390905$	$1263214441/29025$	$0.85169$	$3.39188$	$[1, -1, 0, -24525, 1454800]$	\(y^2+xy=x^3-x^2-24525x+1454800\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$	$1$
327015.ba1	327015ba1	327015.ba	327015ba	$2$	$2$	\( 3^{2} \cdot 5 \cdot 13^{2} \cdot 43 \)	\( 3^{9} \cdot 5^{2} \cdot 13^{6} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.510573043$	$1$		$3$	$1327104$	$1.474432$	$1263214441/29025$	$0.85169$	$3.38156$	$[1, -1, 0, -34254, -2382665]$	\(y^2+xy=x^3-x^2-34254x-2382665\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(374, 5897)]$	$1$
341205.q1	341205q1	341205.q	341205q	$2$	$2$	\( 3 \cdot 5 \cdot 23^{2} \cdot 43 \)	\( 3^{3} \cdot 5^{2} \cdot 23^{6} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$11.25706579$	$1$		$1$	$912384$	$1.210400$	$1263214441/29025$	$0.85169$	$3.12160$	$[1, 1, 0, -11913, -495432]$	\(y^2+xy=x^3+x^2-11913x-495432\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(-189229/58, 498501/58)]$	$1$
390225.bj1	390225bj1	390225.bj	390225bj	$2$	$2$	\( 3 \cdot 5^{2} \cdot 11^{2} \cdot 43 \)	\( 3^{3} \cdot 5^{8} \cdot 11^{6} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$8.280449717$	$1$		$3$	$2419200$	$1.646318$	$1263214441/29025$	$0.85169$	$3.49536$	$[1, 0, 1, -68126, -6712477]$	\(y^2+xy+y=x^3-68126x-6712477\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(43967, 9197016)]$	$1$
416025.t1	416025t1	416025.t	416025t	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 43^{2} \)	\( 3^{9} \cdot 5^{8} \cdot 43^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$11.35770928$	$1$		$1$	$25546752$	$2.877277$	$1263214441/29025$	$0.85169$	$4.61973$	$[1, -1, 1, -9369230, 10819331772]$	\(y^2+xy+y=x^3-x^2-9369230x+10819331772\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(-285566/9, 4710745/9)]$	$1$
443760.t1	443760t1	443760.t	443760t	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 43^{2} \)	\( 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 43^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$7.997640784$	$1$		$1$	$8515584$	$2.216400$	$1263214441/29025$	$0.85169$	$3.98691$	$[0, -1, 0, -666256, 205344256]$	\(y^2=x^3-x^2-666256x+205344256\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(-7208/3, 404632/3)]$	$1$
474075.di1	474075di1	474075.di	474075di	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 43 \)	\( 3^{9} \cdot 5^{8} \cdot 7^{6} \cdot 43 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$13.91399140$	$1$		$5$	$3981312$	$1.969631$	$1263214441/29025$	$0.85169$	$3.74017$	$[1, -1, 0, -248292, 46727491]$	\(y^2+xy=x^3-x^2-248292x+46727491\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(1154, 35423), (450, 4871)]$	$1$

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