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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
4998.a1	4998j2	4998.a	4998j	$2$	$3$	\( 2 \cdot 3 \cdot 7^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{5} \cdot 7^{2} \cdot 17^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$0.412666720$	$1$		$4$	$181440$	$2.291546$	$222165413800219579417/118033833938006016$	$1.07176$	$5.95785$	$[1, 1, 0, -461724, 34374096]$	\(y^2+xy=x^3+x^2-461724x+34374096\)	3.4.0.a.1, 21.8.0-3.a.1.2, 204.8.0.?, 1428.16.0.?	$[(-616, 9556)]$
4998.w1	4998k2	4998.w	4998k	$2$	$3$	\( 2 \cdot 3 \cdot 7^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{5} \cdot 7^{8} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$204$	$16$	$0$	$1$	$1$		$0$	$1270080$	$3.264500$	$222165413800219579417/118033833938006016$	$1.07176$	$7.32873$	$[1, 0, 1, -22624502, -11858188408]$	\(y^2+xy+y=x^3-22624502x-11858188408\)	3.8.0-3.a.1.1, 204.16.0.?	$[ ]$
14994.bp1	14994cd2	14994.bp	14994cd	$2$	$3$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{11} \cdot 7^{8} \cdot 17^{9} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$204$	$16$	$0$	$1$	$1$		$2$	$10160640$	$3.813808$	$222165413800219579417/118033833938006016$	$1.07176$	$7.17691$	$[1, -1, 1, -203620514, 320171087009]$	\(y^2+xy+y=x^3-x^2-203620514x+320171087009\)	3.8.0-3.a.1.2, 204.16.0.?	$[ ]$
14994.da1	14994cq2	14994.da	14994cq	$2$	$3$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{11} \cdot 7^{2} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$1$	$1$		$0$	$1451520$	$2.840851$	$222165413800219579417/118033833938006016$	$1.07176$	$5.96267$	$[1, -1, 1, -4155521, -932256111]$	\(y^2+xy+y=x^3-x^2-4155521x-932256111\)	3.4.0.a.1, 21.8.0-3.a.1.1, 204.8.0.?, 1428.16.0.?	$[ ]$
39984.bw1	39984bf2	39984.bw	39984bf	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( 2^{24} \cdot 3^{5} \cdot 7^{8} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$204$	$16$	$0$	$1$	$49$	$7$	$0$	$30481920$	$3.957649$	$222165413800219579417/118033833938006016$	$1.07176$	$6.67548$	$[0, -1, 0, -361992024, 758924058096]$	\(y^2=x^3-x^2-361992024x+758924058096\)	3.4.0.a.1, 12.8.0-3.a.1.2, 102.8.0.?, 204.16.0.?	$[ ]$
39984.cf1	39984dw2	39984.cf	39984dw	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( 2^{24} \cdot 3^{5} \cdot 7^{2} \cdot 17^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$0.668275857$	$1$		$6$	$4354560$	$2.984692$	$222165413800219579417/118033833938006016$	$1.07176$	$5.57363$	$[0, 1, 0, -7387592, -2214717324]$	\(y^2=x^3+x^2-7387592x-2214717324\)	3.4.0.a.1, 84.8.0.?, 204.8.0.?, 714.8.0.?, 1428.16.0.?	$[(-428, 29478)]$
84966.f1	84966f2	84966.f	84966f	$2$	$3$	\( 2 \cdot 3 \cdot 7^{2} \cdot 17^{2} \)	\( 2^{12} \cdot 3^{5} \cdot 7^{8} \cdot 17^{15} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$204$	$16$	$0$	$23.72453137$	$1$		$0$	$365783040$	$4.681107$	$222165413800219579417/118033833938006016$	$1.07176$	$6.99705$	$[1, 1, 0, -6538480939, -58252741166339]$	\(y^2+xy=x^3+x^2-6538480939x-58252741166339\)	3.4.0.a.1, 12.8.0-3.a.1.3, 51.8.0-3.a.1.1, 204.16.0.?	$[(-870306921709370/129783, 26073396158312816347963/129783)]$
84966.cn1	84966cf2	84966.cn	84966cf	$2$	$3$	\( 2 \cdot 3 \cdot 7^{2} \cdot 17^{2} \)	\( 2^{12} \cdot 3^{5} \cdot 7^{2} \cdot 17^{15} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$8.053079927$	$1$		$0$	$52254720$	$3.708153$	$222165413800219579417/118033833938006016$	$1.07176$	$5.96837$	$[1, 0, 1, -133438387, 169814001998]$	\(y^2+xy+y=x^3-133438387x+169814001998\)	3.4.0.a.1, 84.8.0.?, 204.8.0.?, 357.8.0.?, 1428.16.0.?	$[(-275769/5, 69106064/5)]$
119952.g1	119952eg2	119952.g	119952eg	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{24} \cdot 3^{11} \cdot 7^{8} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$204$	$16$	$0$	$1$	$1$		$0$	$243855360$	$4.506958$	$222165413800219579417/118033833938006016$	$1.07176$	$6.61203$	$[0, 0, 0, -3257928219, -20487691640374]$	\(y^2=x^3-3257928219x-20487691640374\)	3.4.0.a.1, 12.8.0-3.a.1.1, 102.8.0.?, 204.16.0.?	$[ ]$
119952.ga1	119952fo2	119952.ga	119952fo	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{24} \cdot 3^{11} \cdot 7^{2} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$1$	$1$		$0$	$34836480$	$3.534000$	$222165413800219579417/118033833938006016$	$1.07176$	$5.61369$	$[0, 0, 0, -66488331, 59730879418]$	\(y^2=x^3-66488331x+59730879418\)	3.4.0.a.1, 84.8.0.?, 204.8.0.?, 714.8.0.?, 1428.16.0.?	$[ ]$
124950.ek1	124950er2	124950.ek	124950er	$2$	$3$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{5} \cdot 5^{6} \cdot 7^{8} \cdot 17^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1020$	$16$	$0$	$1.797158027$	$1$		$4$	$137168640$	$4.069221$	$222165413800219579417/118033833938006016$	$1.07176$	$6.14144$	$[1, 1, 1, -565612538, -1482273550969]$	\(y^2+xy+y=x^3+x^2-565612538x-1482273550969\)	3.4.0.a.1, 15.8.0-3.a.1.1, 204.8.0.?, 1020.16.0.?	$[(-6199, 1339435)]$
124950.hc1	124950hw2	124950.hc	124950hw	$2$	$3$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{5} \cdot 5^{6} \cdot 7^{2} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$7140$	$16$	$0$	$1$	$1$		$0$	$19595520$	$3.096264$	$222165413800219579417/118033833938006016$	$1.07176$	$5.14657$	$[1, 0, 0, -11543113, 4319848217]$	\(y^2+xy=x^3-11543113x+4319848217\)	3.4.0.a.1, 105.8.0.?, 204.8.0.?, 7140.16.0.?	$[ ]$
159936.y1	159936il2	159936.y	159936il	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( 2^{30} \cdot 3^{5} \cdot 7^{8} \cdot 17^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$408$	$16$	$0$	$24.40791277$	$1$		$0$	$243855360$	$4.304222$	$222165413800219579417/118033833938006016$	$1.07176$	$6.25026$	$[0, -1, 0, -1447968097, -6069944496671]$	\(y^2=x^3-x^2-1447968097x-6069944496671\)	3.4.0.a.1, 24.8.0-3.a.1.1, 204.8.0.?, 408.16.0.?	$[(-56122910889/1285, 4178823125196784/1285)]$
159936.en1	159936et2	159936.en	159936et	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( 2^{30} \cdot 3^{5} \cdot 7^{2} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2856$	$16$	$0$	$1$	$1$		$0$	$34836480$	$3.331268$	$222165413800219579417/118033833938006016$	$1.07176$	$5.27588$	$[0, -1, 0, -29550369, -17688188223]$	\(y^2=x^3-x^2-29550369x-17688188223\)	3.4.0.a.1, 168.8.0.?, 204.8.0.?, 2856.16.0.?	$[ ]$
159936.fm1	159936g2	159936.fm	159936g	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( 2^{30} \cdot 3^{5} \cdot 7^{8} \cdot 17^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$408$	$16$	$0$	$5.549409728$	$1$		$2$	$243855360$	$4.304222$	$222165413800219579417/118033833938006016$	$1.07176$	$6.25026$	$[0, 1, 0, -1447968097, 6069944496671]$	\(y^2=x^3+x^2-1447968097x+6069944496671\)	3.4.0.a.1, 24.8.0-3.a.1.3, 204.8.0.?, 408.16.0.?	$[(-169, 2512896)]$
159936.kp1	159936hu2	159936.kp	159936hu	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( 2^{30} \cdot 3^{5} \cdot 7^{2} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2856$	$16$	$0$	$1$	$1$		$0$	$34836480$	$3.331268$	$222165413800219579417/118033833938006016$	$1.07176$	$5.27588$	$[0, 1, 0, -29550369, 17688188223]$	\(y^2=x^3+x^2-29550369x+17688188223\)	3.4.0.a.1, 168.8.0.?, 204.8.0.?, 2856.16.0.?	$[ ]$
254898.ed1	254898ed2	254898.ed	254898ed	$2$	$3$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} \)	\( 2^{12} \cdot 3^{11} \cdot 7^{2} \cdot 17^{15} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$1$	$1$		$0$	$418037760$	$4.257462$	$222165413800219579417/118033833938006016$	$1.07176$	$5.97116$	$[1, -1, 1, -1200945479, -4584978053953]$	\(y^2+xy+y=x^3-x^2-1200945479x-4584978053953\)	3.4.0.a.1, 84.8.0.?, 204.8.0.?, 357.8.0.?, 1428.16.0.?	$[ ]$
254898.hq1	254898hq2	254898.hq	254898hq	$2$	$3$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} \)	\( 2^{12} \cdot 3^{11} \cdot 7^{8} \cdot 17^{15} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$204$	$16$	$0$	$14.74705858$	$1$		$0$	$2926264320$	$5.230415$	$222165413800219579417/118033833938006016$	$1.07176$	$6.90905$	$[1, -1, 1, -58846328456, 1572765165162699]$	\(y^2+xy+y=x^3-x^2-58846328456x+1572765165162699\)	3.4.0.a.1, 12.8.0-3.a.1.4, 51.8.0-3.a.1.2, 204.16.0.?	$[(-30113899/29, 1470666352413/29)]$
374850.hr1	374850hr2	374850.hr	374850hr	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{11} \cdot 5^{6} \cdot 7^{8} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1020$	$16$	$0$	$1$	$1$		$0$	$1097349120$	$4.618523$	$222165413800219579417/118033833938006016$	$1.07176$	$6.12933$	$[1, -1, 0, -5090512842, 40016295363316]$	\(y^2+xy=x^3-x^2-5090512842x+40016295363316\)	3.4.0.a.1, 15.8.0-3.a.1.2, 204.8.0.?, 1020.16.0.?	$[ ]$
374850.ia1	374850ia2	374850.ia	374850ia	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{11} \cdot 5^{6} \cdot 7^{2} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$7140$	$16$	$0$	$1$	$1$		$0$	$156764160$	$3.645573$	$222165413800219579417/118033833938006016$	$1.07176$	$5.21962$	$[1, -1, 0, -103888017, -116635901859]$	\(y^2+xy=x^3-x^2-103888017x-116635901859\)	3.4.0.a.1, 105.8.0.?, 204.8.0.?, 7140.16.0.?	$[ ]$
479808.o1	479808o2	479808.o	479808o	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{30} \cdot 3^{11} \cdot 7^{2} \cdot 17^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2856$	$16$	$0$	$23.23993521$	$1$		$0$	$278691840$	$3.880573$	$222165413800219579417/118033833938006016$	$1.07176$	$5.33670$	$[0, 0, 0, -265953324, -477847035344]$	\(y^2=x^3-265953324x-477847035344\)	3.4.0.a.1, 168.8.0.?, 204.8.0.?, 2856.16.0.?	$[(-27668776456/2041, 8483454052495092/2041)]$
479808.cv1	479808cv2	479808.cv	479808cv	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{30} \cdot 3^{11} \cdot 7^{2} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2856$	$16$	$0$	$1$	$4$	$2$	$0$	$278691840$	$3.880573$	$222165413800219579417/118033833938006016$	$1.07176$	$5.33670$	$[0, 0, 0, -265953324, 477847035344]$	\(y^2=x^3-265953324x+477847035344\)	3.4.0.a.1, 168.8.0.?, 204.8.0.?, 2856.16.0.?	$[ ]$
479808.pi1	479808pi2	479808.pi	479808pi	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{30} \cdot 3^{11} \cdot 7^{8} \cdot 17^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$408$	$16$	$0$	$2.471347861$	$1$		$2$	$1950842880$	$4.853531$	$222165413800219579417/118033833938006016$	$1.07176$	$6.22924$	$[0, 0, 0, -13031712876, 163901533122992]$	\(y^2=x^3-13031712876x+163901533122992\)	3.4.0.a.1, 24.8.0-3.a.1.2, 204.8.0.?, 408.16.0.?	$[(-70472, 27060804)]$
479808.rt1	479808rt2	479808.rt	479808rt	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( 2^{30} \cdot 3^{11} \cdot 7^{8} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$408$	$16$	$0$	$1$	$4$	$2$	$0$	$1950842880$	$4.853531$	$222165413800219579417/118033833938006016$	$1.07176$	$6.22924$	$[0, 0, 0, -13031712876, -163901533122992]$	\(y^2=x^3-13031712876x-163901533122992\)	3.4.0.a.1, 24.8.0-3.a.1.4, 204.8.0.?, 408.16.0.?	$[ ]$

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