Elliptic curve search results

Results (24 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
1932.b2	1932b2	1932.b	1932b	$2$	$3$	\( 2^{2} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 23^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$966$	$16$	$0$	$1$	$1$		$0$	$35640$	$2.437466$	$-1400832679220224000/150124273180279587$	$1.09251$	$6.94599$	$1$	$[0, 1, 0, -148013, 299020767]$	\(y^2=x^3+x^2-148013x+299020767\)	3.8.0-3.a.1.1, 966.16.0.?	$[ ]$	$1$
5796.d2	5796h2	5796.d	5796h	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{11} \cdot 7^{3} \cdot 23^{9} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$966$	$16$	$0$	$2.151197345$	$1$		$6$	$285120$	$2.986774$	$-1400832679220224000/150124273180279587$	$1.09251$	$6.82605$	$1$	$[0, 0, 0, -1332120, -8074892828]$	\(y^2=x^3-1332120x-8074892828\)	3.8.0-3.a.1.2, 966.16.0.?	$[(2732, 93150)]$	$1$
7728.d2	7728i2	7728.d	7728i	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1932$	$16$	$0$	$2.015690731$	$1$		$2$	$142560$	$2.437466$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.87042$	$1$	$[0, -1, 0, -148013, -299020767]$	\(y^2=x^3-x^2-148013x-299020767\)	3.4.0.a.1, 12.8.0-3.a.1.2, 966.8.0.?, 1932.16.0.?	$[(1509, 53958)]$	$1$
13524.b2	13524e2	13524.b	13524e	$2$	$3$	\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{9} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$966$	$16$	$0$	$29.23441676$	$1$		$0$	$1710720$	$3.410423$	$-1400832679220224000/150124273180279587$	$1.09251$	$6.75247$	$1$	$[0, -1, 0, -7252653, -102578628375]$	\(y^2=x^3-x^2-7252653x-102578628375\)	3.4.0.a.1, 21.8.0-3.a.1.2, 138.8.0.?, 966.16.0.?	$[(148799224741016/17483, 1815071418980981183323/17483)]$	$1$
23184.z2	23184bg2	23184.z	23184bg	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{11} \cdot 7^{3} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1932$	$16$	$0$	$13.63829513$	$1$		$0$	$1140480$	$2.986774$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.88458$	$1$	$[0, 0, 0, -1332120, 8074892828]$	\(y^2=x^3-1332120x+8074892828\)	3.4.0.a.1, 12.8.0-3.a.1.1, 966.8.0.?, 1932.16.0.?	$[(172214/23, 1065965834/23)]$	$1$
30912.r2	30912h2	30912.r	30912h	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{14} \cdot 3^{5} \cdot 7^{3} \cdot 23^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$3864$	$16$	$0$	$1$	$1$		$0$	$1140480$	$2.784042$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.48554$	$1$	$[0, -1, 0, -592053, 2392758189]$	\(y^2=x^3-x^2-592053x+2392758189\)	3.4.0.a.1, 24.8.0-3.a.1.1, 966.8.0.?, 3864.16.0.?	$[ ]$	$1$
30912.bv2	30912bz2	30912.bv	30912bz	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{14} \cdot 3^{5} \cdot 7^{3} \cdot 23^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$3864$	$16$	$0$	$1$	$1$		$0$	$1140480$	$2.784042$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.48554$	$1$	$[0, 1, 0, -592053, -2392758189]$	\(y^2=x^3+x^2-592053x-2392758189\)	3.4.0.a.1, 24.8.0-3.a.1.3, 966.8.0.?, 3864.16.0.?	$[ ]$	$1$
40572.m2	40572x2	40572.m	40572x	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{11} \cdot 7^{9} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$966$	$16$	$0$	$0.625487673$	$1$		$2$	$13685760$	$3.959728$	$-1400832679220224000/150124273180279587$	$1.09251$	$6.67456$	$1$	$[0, 0, 0, -65273880, 2769688240004]$	\(y^2=x^3-65273880x+2769688240004\)	3.4.0.a.1, 21.8.0-3.a.1.1, 138.8.0.?, 966.16.0.?	$[(1645, 1633023)]$	$1$
44436.k2	44436i2	44436.k	44436i	$2$	$3$	\( 2^{2} \cdot 3 \cdot 7 \cdot 23^{2} \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 23^{15} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$966$	$16$	$0$	$1$	$9$	$3$	$0$	$18817920$	$4.005211$	$-1400832679220224000/150124273180279587$	$1.09251$	$6.66883$	$1$	$[0, 1, 0, -78299053, -3638812064065]$	\(y^2=x^3+x^2-78299053x-3638812064065\)	3.4.0.a.1, 42.8.0-3.a.1.2, 69.8.0-3.a.1.1, 966.16.0.?	$[ ]$	$1$
48300.g2	48300e2	48300.g	48300e	$2$	$3$	\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 5^{6} \cdot 7^{3} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$4830$	$16$	$0$	$1.243953355$	$1$		$2$	$5132160$	$3.242188$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.76830$	$1$	$[0, -1, 0, -3700333, 37384996537]$	\(y^2=x^3-x^2-3700333x+37384996537\)	3.4.0.a.1, 15.8.0-3.a.1.1, 966.8.0.?, 4830.16.0.?	$[(-2253, 185150)]$	$1$
54096.cm2	54096de2	54096.cm	54096de	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{9} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1932$	$16$	$0$	$0.621282035$	$1$		$6$	$6842880$	$3.410423$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.89355$	$1$	$[0, 1, 0, -7252653, 102578628375]$	\(y^2=x^3+x^2-7252653x+102578628375\)	3.4.0.a.1, 84.8.0.?, 276.8.0.?, 966.8.0.?, 1932.16.0.?	$[(48687, 10731294)]$	$1$
92736.ck2	92736ds2	92736.ck	92736ds	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( - 2^{14} \cdot 3^{11} \cdot 7^{3} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$3864$	$16$	$0$	$20.94990559$	$1$		$0$	$9123840$	$3.333347$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.53495$	$1$	$[0, 0, 0, -5328480, 64599142624]$	\(y^2=x^3-5328480x+64599142624\)	3.4.0.a.1, 24.8.0-3.a.1.4, 966.8.0.?, 3864.16.0.?	$[(2972650649/1528, 872984846035395/1528)]$	$1$
92736.dk2	92736ci2	92736.dk	92736ci	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( - 2^{14} \cdot 3^{11} \cdot 7^{3} \cdot 23^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$3864$	$16$	$0$	$1$	$1$		$0$	$9123840$	$3.333347$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.53495$	$1$	$[0, 0, 0, -5328480, -64599142624]$	\(y^2=x^3-5328480x-64599142624\)	3.4.0.a.1, 24.8.0-3.a.1.2, 966.8.0.?, 3864.16.0.?	$[ ]$	$1$
133308.l2	133308k2	133308.l	133308k	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 23^{2} \)	\( - 2^{8} \cdot 3^{11} \cdot 7^{3} \cdot 23^{15} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$966$	$16$	$0$	$1$	$1$		$0$	$150543360$	$4.554520$	$-1400832679220224000/150124273180279587$	$1.09251$	$6.60656$	$1$	$[0, 0, 0, -704691480, 98247221038276]$	\(y^2=x^3-704691480x+98247221038276\)	3.4.0.a.1, 42.8.0-3.a.1.1, 69.8.0-3.a.1.2, 966.16.0.?	$[ ]$	$1$
144900.e2	144900bc2	144900.e	144900bc	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{11} \cdot 5^{6} \cdot 7^{3} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$4830$	$16$	$0$	$57.60145420$	$1$		$0$	$41057280$	$3.791492$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.78972$	$1$	$[0, 0, 0, -33303000, -1009361603500]$	\(y^2=x^3-33303000x-1009361603500\)	3.4.0.a.1, 15.8.0-3.a.1.2, 966.8.0.?, 4830.16.0.?	$[(120408622651835208065491765/71356608007, 1228211957521809268895703506940434738925/71356608007)]$	$1$
162288.do2	162288bo2	162288.do	162288bo	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{11} \cdot 7^{9} \cdot 23^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1932$	$16$	$0$	$1$	$4$	$2$	$0$	$54743040$	$3.959728$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.90330$	$1$	$[0, 0, 0, -65273880, -2769688240004]$	\(y^2=x^3-65273880x-2769688240004\)	3.4.0.a.1, 84.8.0.?, 276.8.0.?, 966.8.0.?, 1932.16.0.?	$[ ]$	$1$
177744.ba2	177744bu2	177744.ba	177744bu	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23^{2} \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 23^{15} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1932$	$16$	$0$	$1$	$4$	$2$	$0$	$75271680$	$4.005211$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.90403$	$1$	$[0, -1, 0, -78299053, 3638812064065]$	\(y^2=x^3-x^2-78299053x+3638812064065\)	3.4.0.a.1, 84.8.0.?, 276.8.0.?, 966.8.0.?, 1932.16.0.?	$[ ]$	$1$
193200.gb2	193200z2	193200.gb	193200z	$2$	$3$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 5^{6} \cdot 7^{3} \cdot 23^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$9660$	$16$	$0$	$1$	$1$		$0$	$20528640$	$3.242188$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.11130$	$1$	$[0, 1, 0, -3700333, -37384996537]$	\(y^2=x^3+x^2-3700333x-37384996537\)	3.4.0.a.1, 60.8.0-3.a.1.1, 966.8.0.?, 9660.16.0.?	$[ ]$	$1$
216384.cm2	216384do2	216384.cm	216384do	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( - 2^{14} \cdot 3^{5} \cdot 7^{9} \cdot 23^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$3864$	$16$	$0$	$1$	$1$		$0$	$54743040$	$3.756996$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.56703$	$1$	$[0, -1, 0, -29010613, 820658037613]$	\(y^2=x^3-x^2-29010613x+820658037613\)	3.4.0.a.1, 168.8.0.?, 552.8.0.?, 966.8.0.?, 3864.16.0.?	$[ ]$	$1$
216384.go2	216384fs2	216384.go	216384fs	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( - 2^{14} \cdot 3^{5} \cdot 7^{9} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$3864$	$16$	$0$	$19.40563296$	$1$		$0$	$54743040$	$3.756996$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.56703$	$1$	$[0, 1, 0, -29010613, -820658037613]$	\(y^2=x^3+x^2-29010613x-820658037613\)	3.4.0.a.1, 168.8.0.?, 552.8.0.?, 966.8.0.?, 3864.16.0.?	$[(13246132454/965, 1152552653597667/965)]$	$1$
233772.ba2	233772ba2	233772.ba	233772ba	$2$	$3$	\( 2^{2} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 11^{6} \cdot 23^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$10626$	$16$	$0$	$1$	$1$		$0$	$48114000$	$3.636414$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.41517$	$1$	$[0, 1, 0, -17909613, -398068279281]$	\(y^2=x^3+x^2-17909613x-398068279281\)	3.4.0.a.1, 33.8.0-3.a.1.1, 966.8.0.?, 10626.16.0.?	$[ ]$	$1$
311052.i2	311052i2	311052.i	311052i	$2$	$3$	\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{9} \cdot 23^{15} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$966$	$16$	$0$	$1$	$9$	$3$	$0$	$903260160$	$4.978172$	$-1400832679220224000/150124273180279587$	$1.09251$	$6.56592$	$1$	$[0, -1, 0, -3836653613, 1248104864667081]$	\(y^2=x^3-x^2-3836653613x+1248104864667081\)	3.4.0.a.1, 6.8.0-3.a.1.1, 483.8.0.?, 966.16.0.?	$[ ]$	$1$
326508.t2	326508t2	326508.t	326508t	$2$	$3$	\( 2^{2} \cdot 3 \cdot 7 \cdot 13^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 13^{6} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$12558$	$16$	$0$	$5.697562963$	$1$		$2$	$82114560$	$3.719940$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.35161$	$1$	$[0, 1, 0, -25014253, 657048682031]$	\(y^2=x^3+x^2-25014253x+657048682031\)	3.4.0.a.1, 39.8.0-3.a.1.2, 966.8.0.?, 12558.16.0.?	$[(5594, 831987)]$	$1$
338100.dv2	338100dv2	338100.dv	338100dv	$2$	$3$	\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 5^{6} \cdot 7^{9} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$4830$	$16$	$0$	$1.448458444$	$1$		$4$	$246343680$	$4.215141$	$-1400832679220224000/150124273180279587$	$1.09251$	$5.80371$	$1$	$[0, 1, 0, -181316333, -12822691179537]$	\(y^2=x^3+x^2-181316333x-12822691179537\)	3.4.0.a.1, 105.8.0.?, 690.8.0.?, 966.8.0.?, 4830.16.0.?	$[(121573, 41976150)]$	$1$

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