Elliptic curve search results

Results (23 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
3570.t2	3570t4	3570.t	3570t	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.161	2B	$4080$	$192$	$1$	$1$	$1$		$2$	$36864$	$1.788086$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98174$	$[1, 1, 1, -252620, 48757805]$	\(y^2+xy+y=x^3+x^2-252620x+48757805\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 60.24.0-60.h.1.3, 120.96.0.?, $\ldots$	$[ ]$
10710.a2	10710f3	10710.a	10710f	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{6} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4080$	$192$	$1$	$1$	$1$		$0$	$294912$	$2.337391$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98390$	$[1, -1, 0, -2273580, -1318734320]$	\(y^2+xy=x^3-x^2-2273580x-1318734320\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0-4.c.1.2, 20.12.0-4.c.1.1, $\ldots$	$[ ]$
17850.ba2	17850u4	17850.ba	17850u	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 \)	\( 2^{6} \cdot 3 \cdot 5^{7} \cdot 7^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4080$	$192$	$1$	$5.063589033$	$1$		$2$	$884736$	$2.592804$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98474$	$[1, 0, 1, -6315501, 6107356648]$	\(y^2+xy+y=x^3-6315501x+6107356648\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0-4.c.1.1, 20.12.0-4.c.1.2, $\ldots$	$[(1486, 1367)]$
24990.ca2	24990by4	24990.ca	24990by	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 \)	\( 2^{6} \cdot 3 \cdot 5 \cdot 7^{8} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$28560$	$192$	$1$	$1$	$4$	$2$	$0$	$1769472$	$2.761040$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98525$	$[1, 0, 0, -12378381, -16761062319]$	\(y^2+xy=x^3-12378381x-16761062319\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 28.12.0-4.c.1.2, 56.48.0-8.bb.2.6, $\ldots$	$[ ]$
28560.ds2	28560ef4	28560.ds	28560ef	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{18} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.177	2B	$4080$	$192$	$1$	$1$	$4$	$2$	$1$	$884736$	$2.481232$	$1782900110862842086081/328139630024640$	$0.99949$	$5.58008$	$[0, 1, 0, -4041920, -3128583372]$	\(y^2=x^3+x^2-4041920x-3128583372\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 60.24.0-60.h.1.1, 120.96.0.?, $\ldots$	$[ ]$
53550.du2	53550eb4	53550.du	53550eb	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)	\( 2^{6} \cdot 3^{7} \cdot 5^{7} \cdot 7^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.183	2B	$4080$	$192$	$1$	$0.838446074$	$1$		$8$	$7077888$	$3.142109$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98628$	$[1, -1, 1, -56839505, -164898629503]$	\(y^2+xy+y=x^3-x^2-56839505x-164898629503\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.6, 60.24.0-60.h.1.1, 120.96.0.?, $\ldots$	$[(-4325, 6208)]$
60690.bv2	60690bw4	60690.bv	60690bw	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} \)	\( 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.123	2B	$4080$	$192$	$1$	$1$	$4$	$2$	$0$	$10616832$	$3.204693$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98644$	$[1, 0, 0, -73007186, 240058147140]$	\(y^2+xy=x^3-73007186x+240058147140\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 16.48.0-8.bb.2.6, 60.12.0.h.1, $\ldots$	$[ ]$
74970.bd2	74970by4	74970.bd	74970by	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( 2^{6} \cdot 3^{7} \cdot 5 \cdot 7^{8} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$28560$	$192$	$1$	$1.043411131$	$1$		$6$	$14155776$	$3.310345$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98669$	$[1, -1, 0, -111405429, 452548682613]$	\(y^2+xy=x^3-x^2-111405429x+452548682613\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 60.12.0.h.1, 84.12.0.?, $\ldots$	$[(5889, 23295)]$
85680.db2	85680el4	85680.db	85680el	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{18} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4080$	$192$	$1$	$1$	$4$	$2$	$1$	$7077888$	$3.030540$	$1782900110862842086081/328139630024640$	$0.99949$	$5.62070$	$[0, 0, 0, -36377283, 84435373762]$	\(y^2=x^3-36377283x+84435373762\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0-4.c.1.1, 20.12.0-4.c.1.2, $\ldots$	$[ ]$
114240.cp2	114240gl4	114240.cp	114240gl	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{24} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.225	2B	$4080$	$192$	$1$	$1$	$4$	$2$	$1$	$7077888$	$2.827805$	$1782900110862842086081/328139630024640$	$0.99949$	$5.27296$	$[0, -1, 0, -16167681, -25012499295]$	\(y^2=x^3-x^2-16167681x-25012499295\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.2.2, 60.12.0.h.1, 120.96.0.?, $\ldots$	$[ ]$
114240.fq2	114240dk4	114240.fq	114240dk	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{24} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.210	2B	$4080$	$192$	$1$	$1.754945497$	$1$		$3$	$7077888$	$2.827805$	$1782900110862842086081/328139630024640$	$0.99949$	$5.27296$	$[0, 1, 0, -16167681, 25012499295]$	\(y^2=x^3+x^2-16167681x+25012499295\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.2.1, 60.12.0.h.1, 120.96.0.?, $\ldots$	$[(5099, 274176)]$
124950.ce2	124950bc4	124950.ce	124950bc	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{6} \cdot 3 \cdot 5^{7} \cdot 7^{8} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$28560$	$192$	$1$	$2.301762771$	$1$		$2$	$42467328$	$3.565758$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98727$	$[1, 1, 0, -309459525, -2095132789875]$	\(y^2+xy=x^3+x^2-309459525x-2095132789875\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 60.12.0.h.1, 84.12.0.?, $\ldots$	$[(-10070, 15235)]$
142800.b2	142800ei4	142800.b	142800ei	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 \)	\( 2^{18} \cdot 3 \cdot 5^{7} \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4080$	$192$	$1$	$1$	$4$	$2$	$1$	$21233664$	$3.285950$	$1782900110862842086081/328139630024640$	$0.99949$	$5.63702$	$[0, -1, 0, -101048008, -390870825488]$	\(y^2=x^3-x^2-101048008x-390870825488\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0-4.c.1.2, 20.12.0-4.c.1.1, $\ldots$	$[ ]$
182070.bw2	182070ct4	182070.bw	182070ct	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17^{2} \)	\( 2^{6} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4080$	$192$	$1$	$1$	$16$	$2$	$0$	$84934656$	$3.753998$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98767$	$[1, -1, 0, -657064674, -6481569972780]$	\(y^2+xy=x^3-x^2-657064674x-6481569972780\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 48.48.0-8.bb.2.4, 60.12.0.h.1, $\ldots$	$[ ]$
199920.c2	199920cy3	199920.c	199920cy	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 \)	\( 2^{18} \cdot 3 \cdot 5 \cdot 7^{8} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$28560$	$192$	$1$	$7.123502252$	$1$		$3$	$42467328$	$3.454189$	$1782900110862842086081/328139630024640$	$0.99949$	$5.64703$	$[0, -1, 0, -198054096, 1072707988416]$	\(y^2=x^3-x^2-198054096x+1072707988416\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 28.12.0-4.c.1.1, 56.48.0-8.bb.2.5, $\ldots$	$[(8378, 37414)]$
303450.b2	303450b3	303450.b	303450b	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17^{2} \)	\( 2^{6} \cdot 3 \cdot 5^{7} \cdot 7^{2} \cdot 17^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4080$	$192$	$1$	$2.848801213$	$1$		$6$	$254803968$	$4.009415$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98816$	$[1, 1, 0, -1825179650, 30007268392500]$	\(y^2+xy=x^3+x^2-1825179650x+30007268392500\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 48.48.0-8.bb.2.7, 60.12.0.h.1, $\ldots$	$[(24940, 16430)]$
342720.ld2	342720ld4	342720.ld	342720ld	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{24} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4080$	$192$	$1$	$20.46886712$	$1$		$1$	$56623104$	$3.377113$	$1782900110862842086081/328139630024640$	$0.99949$	$5.33563$	$[0, 0, 0, -145509132, -675482990096]$	\(y^2=x^3-145509132x-675482990096\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 24.48.0-8.bb.2.2, 40.48.0-8.bb.2.1, $\ldots$	$[(-9295690831/1160, 10070690648553/1160)]$
342720.md2	342720md3	342720.md	342720md	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{24} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4080$	$192$	$1$	$9.441015628$	$1$		$3$	$56623104$	$3.377113$	$1782900110862842086081/328139630024640$	$0.99949$	$5.33563$	$[0, 0, 0, -145509132, 675482990096]$	\(y^2=x^3-145509132x+675482990096\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 24.48.0-8.bb.2.1, 40.48.0-8.bb.2.2, $\ldots$	$[(68540, 17682896)]$
374850.jf2	374850jf3	374850.jf	374850jf	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{6} \cdot 3^{7} \cdot 5^{7} \cdot 7^{8} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$28560$	$192$	$1$	$1$	$1$		$0$	$339738624$	$4.115067$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98836$	$[1, -1, 1, -2785135730, 56565800190897]$	\(y^2+xy+y=x^3-x^2-2785135730x+56565800190897\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 28.12.0-4.c.1.1, 56.48.0-8.bb.2.4, $\ldots$	$[ ]$
424830.fi2	424830fi4	424830.fi	424830fi	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	\( 2^{6} \cdot 3 \cdot 5 \cdot 7^{8} \cdot 17^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$28560$	$192$	$1$	$1$	$4$	$2$	$0$	$509607936$	$4.177650$	$1782900110862842086081/328139630024640$	$0.99949$	$5.98847$	$[1, 1, 1, -3577352115, -82343521821135]$	\(y^2+xy+y=x^3+x^2-3577352115x-82343521821135\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 60.12.0.h.1, 112.48.0.?, $\ldots$	$[ ]$
428400.gi2	428400gi3	428400.gi	428400gi	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)	\( 2^{18} \cdot 3^{7} \cdot 5^{7} \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.167	2B	$4080$	$192$	$1$	$1$	$1$		$3$	$169869312$	$3.835258$	$1782900110862842086081/328139630024640$	$0.99949$	$5.66777$	$[0, 0, 0, -909432075, 10554421720250]$	\(y^2=x^3-909432075x+10554421720250\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.5, 60.24.0-60.h.1.3, 120.96.0.?, $\ldots$	$[ ]$
431970.y2	431970y4	431970.y	431970y	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 17 \)	\( 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{6} \cdot 17^{8} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$44880$	$192$	$1$	$20.28374186$	$1$		$8$	$47185920$	$2.987034$	$1782900110862842086081/328139630024640$	$0.99949$	$4.87973$	$[1, 1, 0, -30567022, -65049473804]$	\(y^2+xy=x^3+x^2-30567022x-65049473804\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 44.12.0-4.c.1.2, 60.12.0.h.1, $\ldots$	$[(-3195, 4804), (-3169, -673)]$
485520.bg2	485520bg4	485520.bg	485520bg	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} \)	\( 2^{18} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.128	2B	$4080$	$192$	$1$	$1$	$16$	$2$	$1$	$254803968$	$3.897839$	$1782900110862842086081/328139630024640$	$0.99949$	$5.67095$	$[0, -1, 0, -1168114976, -15363721416960]$	\(y^2=x^3-x^2-1168114976x-15363721416960\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 16.48.0-8.bb.2.5, 60.12.0.h.1, $\ldots$	$[ ]$

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