Elliptic curve search results

Results (36 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
3675.e1	3675b1	3675.e	3675b	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 3^{5} \cdot 5^{2} \cdot 7^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$3.947563272$	$1$		$2$	$2520$	$0.707505$	$-46585/243$	$0.91462$	$3.87842$	$1$	$[1, 1, 1, -393, -9654]$	\(y^2+xy+y=x^3+x^2-393x-9654\)	6.2.0.a.1	$[(36, 138)]$	$1$
3675.g1	3675k1	3675.g	3675k	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 3^{5} \cdot 5^{2} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.201144133$	$1$		$6$	$360$	$-0.265450$	$-46585/243$	$0.91462$	$2.45620$	$1$	$[1, 0, 0, -8, 27]$	\(y^2+xy=x^3-8x+27\)	6.2.0.a.1	$[(1, 4)]$	$1$
3675.k1	3675g1	3675.k	3675g	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 3^{5} \cdot 5^{8} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1.011115733$	$1$		$2$	$1800$	$0.539269$	$-46585/243$	$0.91462$	$3.63250$	$1$	$[1, 1, 0, -200, 3375]$	\(y^2+xy=x^3+x^2-200x+3375\)	6.2.0.a.1	$[(10, 45)]$	$1$
3675.m1	3675o1	3675.m	3675o	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 3^{5} \cdot 5^{8} \cdot 7^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1.519059052$	$1$		$2$	$12600$	$1.512224$	$-46585/243$	$0.91462$	$5.05472$	$1$	$[1, 0, 1, -9826, -1187077]$	\(y^2+xy+y=x^3-9826x-1187077\)	6.2.0.a.1	$[(151, 806)]$	$1$
11025.k1	11025bi1	11025.k	11025bi	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 3^{11} \cdot 5^{8} \cdot 7^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.564323025$	$1$		$6$	$100800$	$2.061531$	$-46585/243$	$0.91462$	$5.16629$	$1$	$[1, -1, 1, -88430, 32051072]$	\(y^2+xy+y=x^3-x^2-88430x+32051072\)	6.2.0.a.1	$[(-306, 5665)]$	$1$
11025.n1	11025bm1	11025.n	11025bm	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 3^{11} \cdot 5^{8} \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$14400$	$1.088575$	$-46585/243$	$0.91462$	$3.91194$	$1$	$[1, -1, 1, -1805, -92928]$	\(y^2+xy+y=x^3-x^2-1805x-92928\)	6.2.0.a.1	$[ ]$	$1$
11025.bf1	11025w1	11025.bf	11025w	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 3^{11} \cdot 5^{2} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$3.466573304$	$1$		$2$	$2880$	$0.283856$	$-46585/243$	$0.91462$	$2.87447$	$1$	$[1, -1, 0, -72, -729]$	\(y^2+xy=x^3-x^2-72x-729\)	6.2.0.a.1	$[(90, 801)]$	$1$
11025.bi1	11025r1	11025.bi	11025r	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 3^{11} \cdot 5^{2} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$20160$	$1.256811$	$-46585/243$	$0.91462$	$4.12883$	$1$	$[1, -1, 0, -3537, 257116]$	\(y^2+xy=x^3-x^2-3537x+257116\)	6.2.0.a.1	$[ ]$	$1$
58800.ca1	58800gl1	58800.ca	58800gl	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{12} \cdot 3^{5} \cdot 5^{8} \cdot 7^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$5.362121987$	$1$		$2$	$806400$	$2.205372$	$-46585/243$	$0.91462$	$4.53597$	$1$	$[0, -1, 0, -157208, 75972912]$	\(y^2=x^3-x^2-157208x+75972912\)	6.2.0.a.1	$[(588, 13656)]$	$1$
58800.cb1	58800fg1	58800.cb	58800fg	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{12} \cdot 3^{5} \cdot 5^{2} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1.814781131$	$1$		$4$	$23040$	$0.427697$	$-46585/243$	$0.91462$	$2.59349$	$1$	$[0, -1, 0, -128, -1728]$	\(y^2=x^3-x^2-128x-1728\)	6.2.0.a.1	$[(16, 8)]$	$1$
58800.ia1	58800hq1	58800.ia	58800hq	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{12} \cdot 3^{5} \cdot 5^{2} \cdot 7^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.263084932$	$1$		$6$	$161280$	$1.400652$	$-46585/243$	$0.91462$	$3.65665$	$1$	$[0, 1, 0, -6288, 605268]$	\(y^2=x^3+x^2-6288x+605268\)	6.2.0.a.1	$[(114, 1176)]$	$1$
58800.ib1	58800jm1	58800.ib	58800jm	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{12} \cdot 3^{5} \cdot 5^{8} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.456191174$	$1$		$6$	$115200$	$1.232416$	$-46585/243$	$0.91462$	$3.47281$	$1$	$[0, 1, 0, -3208, -222412]$	\(y^2=x^3+x^2-3208x-222412\)	6.2.0.a.1	$[(158, 1800)]$	$1$
176400.iz1	176400da1	176400.iz	176400da	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{12} \cdot 3^{11} \cdot 5^{8} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$6451200$	$2.754677$	$-46585/243$	$0.91462$	$4.66911$	$1$	$[0, 0, 0, -1414875, -2049853750]$	\(y^2=x^3-1414875x-2049853750\)	6.2.0.a.1	$[ ]$	$1$
176400.ja1	176400fg1	176400.ja	176400fg	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{12} \cdot 3^{11} \cdot 5^{2} \cdot 7^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1.098814321$	$1$		$10$	$184320$	$0.977003$	$-46585/243$	$0.91462$	$2.90328$	$1$	$[0, 0, 0, -1155, 47810]$	\(y^2=x^3-1155x+47810\)	6.2.0.a.1	$[(121, 1296), (-41, 162)]$	$1$
176400.lt1	176400hu1	176400.lt	176400hu	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{12} \cdot 3^{11} \cdot 5^{2} \cdot 7^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$2.457942999$	$1$		$2$	$1290240$	$1.949959$	$-46585/243$	$0.91462$	$3.86975$	$1$	$[0, 0, 0, -56595, -16398830]$	\(y^2=x^3-56595x-16398830\)	6.2.0.a.1	$[(441, 6664)]$	$1$
176400.lu1	176400bu1	176400.lu	176400bu	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{12} \cdot 3^{11} \cdot 5^{8} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$3.191473683$	$1$		$2$	$921600$	$1.781723$	$-46585/243$	$0.91462$	$3.70264$	$1$	$[0, 0, 0, -28875, 5976250]$	\(y^2=x^3-28875x+5976250\)	6.2.0.a.1	$[(149, 2232)]$	$1$
235200.gf1	235200gf1	235200.gf	235200gf	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{8} \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$921600$	$1.578989$	$-46585/243$	$0.91462$	$3.41982$	$1$	$[0, -1, 0, -12833, -1766463]$	\(y^2=x^3-x^2-12833x-1766463\)	6.2.0.a.1	$[ ]$	$1$
235200.gg1	235200gg1	235200.gg	235200gg	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{2} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$1290240$	$1.747227$	$-46585/243$	$0.91462$	$3.58305$	$1$	$[0, -1, 0, -25153, 4867297]$	\(y^2=x^3-x^2-25153x+4867297\)	6.2.0.a.1	$[ ]$	$1$
235200.if1	235200if1	235200.if	235200if	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{8} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$6451200$	$2.551945$	$-46585/243$	$0.91462$	$4.36381$	$1$	$[0, -1, 0, -628833, -607154463]$	\(y^2=x^3-x^2-628833x-607154463\)	6.2.0.a.1	$[ ]$	$1$
235200.ig1	235200ig1	235200.ig	235200ig	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{2} \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$184320$	$0.774271$	$-46585/243$	$0.91462$	$2.63905$	$1$	$[0, -1, 0, -513, 14337]$	\(y^2=x^3-x^2-513x+14337\)	6.2.0.a.1	$[ ]$	$1$
235200.ut1	235200ut1	235200.ut	235200ut	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{2} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$1290240$	$1.747227$	$-46585/243$	$0.91462$	$3.58305$	$1$	$[0, 1, 0, -25153, -4867297]$	\(y^2=x^3+x^2-25153x-4867297\)	6.2.0.a.1	$[ ]$	$1$
235200.uu1	235200uu1	235200.uu	235200uu	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{8} \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$921600$	$1.578989$	$-46585/243$	$0.91462$	$3.41982$	$1$	$[0, 1, 0, -12833, 1766463]$	\(y^2=x^3+x^2-12833x+1766463\)	6.2.0.a.1	$[ ]$	$1$
235200.wt1	235200wt1	235200.wt	235200wt	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{2} \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$184320$	$0.774271$	$-46585/243$	$0.91462$	$2.63905$	$1$	$[0, 1, 0, -513, -14337]$	\(y^2=x^3+x^2-513x-14337\)	6.2.0.a.1	$[ ]$	$1$
235200.wu1	235200wu1	235200.wu	235200wu	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{8} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$6451200$	$2.551945$	$-46585/243$	$0.91462$	$4.36381$	$1$	$[0, 1, 0, -628833, 607154463]$	\(y^2=x^3+x^2-628833x+607154463\)	6.2.0.a.1	$[ ]$	$1$
444675.bq1	444675bq1	444675.bq	444675bq	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 3^{5} \cdot 5^{8} \cdot 7^{2} \cdot 11^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$2592000$	$1.738216$	$-46585/243$	$0.91462$	$3.39926$	$1$	$[1, 1, 1, -24263, -4613344]$	\(y^2+xy+y=x^3+x^2-24263x-4613344\)	6.2.0.a.1	$[ ]$	$1$
444675.cy1	444675cy1	444675.cy	444675cy	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 3^{5} \cdot 5^{8} \cdot 7^{8} \cdot 11^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$18144000$	$2.711170$	$-46585/243$	$0.91462$	$4.29702$	$1$	$[1, 0, 0, -1188888, 1578810267]$	\(y^2+xy=x^3-1188888x+1578810267\)	6.2.0.a.1	$[ ]$	$1$
444675.fl1	444675fl1	444675.fl	444675fl	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 3^{5} \cdot 5^{2} \cdot 7^{8} \cdot 11^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$3628800$	$1.906452$	$-46585/243$	$0.91462$	$3.55449$	$1$	$[1, 1, 0, -47555, 12611460]$	\(y^2+xy=x^3+x^2-47555x+12611460\)	6.2.0.a.1	$[ ]$	$1$
444675.gn1	444675gn1	444675.gn	444675gn	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 3^{5} \cdot 5^{2} \cdot 7^{2} \cdot 11^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$518400$	$0.933497$	$-46585/243$	$0.91462$	$2.65673$	$1$	$[1, 0, 1, -971, -36907]$	\(y^2+xy+y=x^3-971x-36907\)	6.2.0.a.1	$[ ]$	$1$
705600.xs1	-	705600.xs	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{11} \cdot 5^{8} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1.162025998$	$1$		$2$	$7372800$	$2.128296$	$-46585/243$	$0.91462$	$3.63031$	$1$	$[0, 0, 0, -115500, 47810000]$	\(y^2=x^3-115500x+47810000\)	6.2.0.a.1	$[(400, 8100)]$
705600.xt1	-	705600.xt	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{11} \cdot 5^{2} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$10321920$	$2.296532$	$-46585/243$	$0.91462$	$3.78022$	$1$	$[0, 0, 0, -226380, 131190640]$	\(y^2=x^3-226380x+131190640\)	6.2.0.a.1	$[ ]$
705600.xu1	-	705600.xu	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{11} \cdot 5^{8} \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$7372800$	$2.128296$	$-46585/243$	$0.91462$	$3.63031$	$1$	$[0, 0, 0, -115500, -47810000]$	\(y^2=x^3-115500x-47810000\)	6.2.0.a.1	$[ ]$
705600.xv1	-	705600.xv	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{11} \cdot 5^{2} \cdot 7^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$3.845133178$	$1$		$2$	$10321920$	$2.296532$	$-46585/243$	$0.91462$	$3.78022$	$1$	$[0, 0, 0, -226380, -131190640]$	\(y^2=x^3-226380x-131190640\)	6.2.0.a.1	$[(736, 10044)]$
705600.beq1	-	705600.beq	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{11} \cdot 5^{8} \cdot 7^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$3.544774145$	$1$		$2$	$51609600$	$3.101250$	$-46585/243$	$0.91462$	$4.49729$	$1$	$[0, 0, 0, -5659500, 16398830000]$	\(y^2=x^3-5659500x+16398830000\)	6.2.0.a.1	$[(9604, 920808)]$
705600.ber1	-	705600.ber	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{11} \cdot 5^{2} \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$1474560$	$1.323578$	$-46585/243$	$0.91462$	$2.91324$	$1$	$[0, 0, 0, -4620, 382480]$	\(y^2=x^3-4620x+382480\)	6.2.0.a.1	$[ ]$
705600.bes1	-	705600.bes	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{11} \cdot 5^{8} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$51609600$	$3.101250$	$-46585/243$	$0.91462$	$4.49729$	$1$	$[0, 0, 0, -5659500, -16398830000]$	\(y^2=x^3-5659500x-16398830000\)	6.2.0.a.1	$[ ]$
705600.bet1	-	705600.bet	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{18} \cdot 3^{11} \cdot 5^{2} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$4.802664959$	$1$		$2$	$1474560$	$1.323578$	$-46585/243$	$0.91462$	$2.91324$	$1$	$[0, 0, 0, -4620, -382480]$	\(y^2=x^3-4620x-382480\)	6.2.0.a.1	$[(2836, 150984)]$

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