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.e2	645b2	645.e	645b	$2$	$2$	\( 3 \cdot 5 \cdot 43 \)	\( - 3^{6} \cdot 5 \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$144$	$-0.010775$	$1685159/6739605$	$1.19354$	$3.58281$	$[1, 1, 0, 3, 126]$	\(y^2+xy=x^3+x^2+3x+126\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
1935.d2	1935f2	1935.d	1935f	$2$	$2$	\( 3^{2} \cdot 5 \cdot 43 \)	\( - 3^{12} \cdot 5 \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$1152$	$0.538531$	$1685159/6739605$	$1.19354$	$3.93371$	$[1, -1, 1, 22, -3378]$	\(y^2+xy+y=x^3-x^2+22x-3378\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
3225.c2	3225g2	3225.c	3225g	$2$	$2$	\( 3 \cdot 5^{2} \cdot 43 \)	\( - 3^{6} \cdot 5^{7} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$0.227097337$	$1$		$12$	$3456$	$0.793944$	$1685159/6739605$	$1.19354$	$4.06436$	$[1, 0, 0, 62, 15617]$	\(y^2+xy=x^3+62x+15617\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-13, 119)]$	$1$
9675.q2	9675o2	9675.q	9675o	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 43 \)	\( - 3^{12} \cdot 5^{7} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$3.935942950$	$1$		$0$	$27648$	$1.343250$	$1685159/6739605$	$1.19354$	$4.29608$	$[1, -1, 0, 558, -421659]$	\(y^2+xy=x^3-x^2+558x-421659\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(807/2, 21639/2)]$	$1$
10320.be2	10320bj2	10320.be	10320bj	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{12} \cdot 3^{6} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.592282229$	$1$		$5$	$9216$	$0.682373$	$1685159/6739605$	$1.19354$	$3.40796$	$[0, 1, 0, 40, -7980]$	\(y^2=x^3+x^2+40x-7980\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(28, 126)]$	$1$
27735.c2	27735i2	27735.c	27735i	$2$	$2$	\( 3 \cdot 5 \cdot 43^{2} \)	\( - 3^{6} \cdot 5 \cdot 43^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.581862919$	$1$		$2$	$266112$	$1.869825$	$1685159/6739605$	$1.19354$	$4.47148$	$[1, 0, 0, 4584, -9929619]$	\(y^2+xy=x^3+4584x-9929619\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(2820, 148359)]$	$1$
30960.a2	30960br2	30960.a	30960br	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{12} \cdot 3^{12} \cdot 5 \cdot 43^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$3.409325971$	$1$		$13$	$73728$	$1.231678$	$1685159/6739605$	$1.19354$	$3.68335$	$[0, 0, 0, 357, 215818]$	\(y^2=x^3+357x+215818\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(71, 774), (266, 4374)]$	$1$
31605.x2	31605r2	31605.x	31605r	$2$	$2$	\( 3 \cdot 5 \cdot 7^{2} \cdot 43 \)	\( - 3^{6} \cdot 5 \cdot 7^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.305458849$	$1$		$4$	$41472$	$0.962180$	$1685159/6739605$	$1.19354$	$3.36389$	$[1, 0, 1, 121, -42829]$	\(y^2+xy+y=x^3+121x-42829\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(39, 127)]$	$1$
41280.a2	41280cb2	41280.a	41280cb	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{18} \cdot 3^{6} \cdot 5 \cdot 43^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$4.253364268$	$1$		$15$	$73728$	$1.028946$	$1685159/6739605$	$1.19354$	$3.35475$	$[0, -1, 0, 159, -63999]$	\(y^2=x^3-x^2+159x-63999\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(93, 864), (2685, 139104)]$	$1$
41280.cq2	41280bh2	41280.cq	41280bh	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{18} \cdot 3^{6} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.992327099$	$1$		$5$	$73728$	$1.028946$	$1685159/6739605$	$1.19354$	$3.35475$	$[0, 1, 0, 159, 63999]$	\(y^2=x^3+x^2+159x+63999\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-3, 252)]$	$1$
51600.by2	51600bv2	51600.by	51600bv	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{12} \cdot 3^{6} \cdot 5^{7} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$221184$	$1.487091$	$1685159/6739605$	$1.19354$	$3.79241$	$[0, -1, 0, 992, -999488]$	\(y^2=x^3-x^2+992x-999488\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
78045.d2	78045j2	78045.d	78045j	$2$	$2$	\( 3 \cdot 5 \cdot 11^{2} \cdot 43 \)	\( - 3^{6} \cdot 5 \cdot 11^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$201600$	$1.188173$	$1685159/6739605$	$1.19354$	$3.33469$	$[1, 1, 1, 300, -166110]$	\(y^2+xy+y=x^3+x^2+300x-166110\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
83205.r2	83205t2	83205.r	83205t	$2$	$2$	\( 3^{2} \cdot 5 \cdot 43^{2} \)	\( - 3^{12} \cdot 5 \cdot 43^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$4$	$2$	$0$	$2128896$	$2.419132$	$1685159/6739605$	$1.19354$	$4.61971$	$[1, -1, 0, 41256, 268099713]$	\(y^2+xy=x^3-x^2+41256x+268099713\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
94815.m2	94815bg2	94815.m	94815bg	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 43 \)	\( - 3^{12} \cdot 5 \cdot 7^{6} \cdot 43^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.470670776$	$1$		$12$	$331776$	$1.511486$	$1685159/6739605$	$1.19354$	$3.61661$	$[1, -1, 1, 1093, 1156376]$	\(y^2+xy+y=x^3-x^2+1093x+1156376\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-26, 1066), (30, 1087)]$	$1$
109005.b2	109005a2	109005.b	109005a	$2$	$2$	\( 3 \cdot 5 \cdot 13^{2} \cdot 43 \)	\( - 3^{6} \cdot 5 \cdot 13^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.079275788$	$1$		$4$	$331776$	$1.271700$	$1685159/6739605$	$1.19354$	$3.32505$	$[1, 1, 1, 419, 274568]$	\(y^2+xy+y=x^3+x^2+419x+274568\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-21, 517)]$	$1$
123840.dy2	123840gd2	123840.dy	123840gd	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{18} \cdot 3^{12} \cdot 5 \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$589824$	$1.578253$	$1685159/6739605$	$1.19354$	$3.60257$	$[0, 0, 0, 1428, 1726544]$	\(y^2=x^3+1428x+1726544\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
123840.gf2	123840di2	123840.gf	123840di	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{18} \cdot 3^{12} \cdot 5 \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$4$	$2$	$1$	$589824$	$1.578253$	$1685159/6739605$	$1.19354$	$3.60257$	$[0, 0, 0, 1428, -1726544]$	\(y^2=x^3+1428x-1726544\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
138675.r2	138675v2	138675.r	138675v	$2$	$2$	\( 3 \cdot 5^{2} \cdot 43^{2} \)	\( - 3^{6} \cdot 5^{7} \cdot 43^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$6386688$	$2.674545$	$1685159/6739605$	$1.19354$	$4.67926$	$[1, 1, 0, 114600, -1241202375]$	\(y^2+xy=x^3+x^2+114600x-1241202375\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
154800.fv2	154800dh2	154800.fv	154800dh	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 43 \)	\( - 2^{12} \cdot 3^{12} \cdot 5^{7} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$3.924190380$	$1$		$5$	$1769472$	$2.036396$	$1685159/6739605$	$1.19354$	$3.99536$	$[0, 0, 0, 8925, 26977250]$	\(y^2=x^3+8925x+26977250\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-265, 2450)]$	$1$
158025.f2	158025m2	158025.f	158025m	$2$	$2$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 43 \)	\( - 3^{6} \cdot 5^{7} \cdot 7^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.083800539$	$1$		$4$	$995328$	$1.766899$	$1685159/6739605$	$1.19354$	$3.71832$	$[1, 1, 1, 3037, -5353594]$	\(y^2+xy+y=x^3+x^2+3037x-5353594\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(244, 3038)]$	$1$
186405.g2	186405h2	186405.g	186405h	$2$	$2$	\( 3 \cdot 5 \cdot 17^{2} \cdot 43 \)	\( - 3^{6} \cdot 5 \cdot 17^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$746496$	$1.405832$	$1685159/6739605$	$1.19354$	$3.31068$	$[1, 0, 1, 716, 613667]$	\(y^2+xy+y=x^3+716x+613667\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
206400.l2	206400iz2	206400.l	206400iz	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{18} \cdot 3^{6} \cdot 5^{7} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$3.669212022$	$1$		$3$	$1769472$	$1.833666$	$1685159/6739605$	$1.19354$	$3.70264$	$[0, -1, 0, 3967, 7991937]$	\(y^2=x^3-x^2+3967x+7991937\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(207, 4200)]$	$1$
206400.kg2	206400cl2	206400.kg	206400cl	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{18} \cdot 3^{6} \cdot 5^{7} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$1769472$	$1.833666$	$1685159/6739605$	$1.19354$	$3.70264$	$[0, 1, 0, 3967, -7991937]$	\(y^2=x^3+x^2+3967x-7991937\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
232845.h2	232845h2	232845.h	232845h	$2$	$2$	\( 3 \cdot 5 \cdot 19^{2} \cdot 43 \)	\( - 3^{6} \cdot 5 \cdot 19^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$943488$	$1.461445$	$1685159/6739605$	$1.19354$	$3.30509$	$[1, 0, 0, 895, -856578]$	\(y^2+xy=x^3+895x-856578\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
234135.y2	234135y2	234135.y	234135y	$2$	$2$	\( 3^{2} \cdot 5 \cdot 11^{2} \cdot 43 \)	\( - 3^{12} \cdot 5 \cdot 11^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$1612800$	$1.737480$	$1685159/6739605$	$1.19354$	$3.57153$	$[1, -1, 0, 2700, 4487665]$	\(y^2+xy=x^3-x^2+2700x+4487665\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$	$1$
327015.ba2	327015ba2	327015.ba	327015ba	$2$	$2$	\( 3^{2} \cdot 5 \cdot 13^{2} \cdot 43 \)	\( - 3^{12} \cdot 5 \cdot 13^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$5.021146086$	$1$		$0$	$2654208$	$1.821007$	$1685159/6739605$	$1.19354$	$3.55649$	$[1, -1, 0, 3771, -7409570]$	\(y^2+xy=x^3-x^2+3771x-7409570\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(1431/2, 48931/2)]$	$1$
341205.q2	341205q2	341205.q	341205q	$2$	$2$	\( 3 \cdot 5 \cdot 23^{2} \cdot 43 \)	\( - 3^{6} \cdot 5 \cdot 23^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$5.628532895$	$1$		$2$	$1824768$	$1.556973$	$1685159/6739605$	$1.19354$	$3.29594$	$[1, 1, 0, 1312, -1519047]$	\(y^2+xy=x^3+x^2+1312x-1519047\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(41896, 8554671)]$	$1$
390225.bj2	390225bj2	390225.bj	390225bj	$2$	$2$	\( 3 \cdot 5^{2} \cdot 11^{2} \cdot 43 \)	\( - 3^{6} \cdot 5^{7} \cdot 11^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$4.140224858$	$1$		$4$	$4838400$	$1.992891$	$1685159/6739605$	$1.19354$	$3.66788$	$[1, 0, 1, 7499, -20778727]$	\(y^2+xy+y=x^3+7499x-20778727\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(267, 391)]$	$1$
416025.t2	416025t2	416025.t	416025t	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 43^{2} \)	\( - 3^{12} \cdot 5^{7} \cdot 43^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$5.678854640$	$1$		$0$	$51093504$	$3.223850$	$1685159/6739605$	$1.19354$	$4.79140$	$[1, -1, 1, 1031395, 33513495522]$	\(y^2+xy+y=x^3-x^2+1031395x+33513495522\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(118316/7, 76342335/7)]$	$1$
443760.t2	443760t2	443760.t	443760t	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 43^{2} \)	\( - 2^{12} \cdot 3^{6} \cdot 5 \cdot 43^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$15.99528156$	$1$		$1$	$17031168$	$2.562973$	$1685159/6739605$	$1.19354$	$4.15772$	$[0, -1, 0, 73344, 635495616]$	\(y^2=x^3-x^2+73344x+635495616\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-8370062/111, 22543166926/111)]$	$1$
474075.di2	474075di2	474075.di	474075di	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 43 \)	\( - 3^{12} \cdot 5^{7} \cdot 7^{6} \cdot 43^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$3.478497850$	$1$		$10$	$7962624$	$2.316204$	$1685159/6739605$	$1.19354$	$3.91012$	$[1, -1, 0, 27333, 144574366]$	\(y^2+xy=x^3-x^2+27333x+144574366\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-346, 9848), (-82, 11948)]$	$1$

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