Elliptic curve search results

Results (26 matches)

  Download displayed columns for results to

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
3192.p2	3192g2	3192.p	3192g	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{11} \cdot 3^{14} \cdot 7^{5} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$3.922377163$	$1$		$3$	$188160$	$2.897152$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$7.23271$	$[0, 1, 0, -4283112, -5439217680]$	\(y^2=x^3+x^2-4283112x-5439217680\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(15531, 1916910)]$
6384.o2	6384d2	6384.o	6384d	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{11} \cdot 3^{14} \cdot 7^{5} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$376320$	$2.897152$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.66051$	$[0, -1, 0, -4283112, 5439217680]$	\(y^2=x^3-x^2-4283112x+5439217680\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
9576.f2	9576x2	9576.f	9576x	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{11} \cdot 3^{20} \cdot 7^{5} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$4$	$2$	$1$	$1505280$	$3.446457$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$7.08498$	$[0, 0, 0, -38548011, 146820329350]$	\(y^2=x^3-38548011x+146820329350\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
19152.g2	19152x2	19152.g	19152x	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{11} \cdot 3^{20} \cdot 7^{5} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$6.401484667$	$1$		$3$	$3010560$	$3.446457$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.58692$	$[0, 0, 0, -38548011, -146820329350]$	\(y^2=x^3-38548011x-146820329350\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(8447, 360934)]$
22344.f2	22344d2	22344.f	22344d	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{11} \cdot 3^{14} \cdot 7^{11} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$9031680$	$3.870106$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.99318$	$[0, -1, 0, -209872504, 1865231919244]$	\(y^2=x^3-x^2-209872504x+1865231919244\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
25536.l2	25536d2	25536.l	25536d	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{17} \cdot 3^{14} \cdot 7^{5} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$56.48772123$	$1$		$1$	$3010560$	$3.243725$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.16045$	$[0, -1, 0, -17132449, -43496608991]$	\(y^2=x^3-x^2-17132449x-43496608991\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(3328059054872703801825440/5481669751, 6067001735450365996965766835761424793/5481669751)]$
25536.cg2	25536dr2	25536.cg	25536dr	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{17} \cdot 3^{14} \cdot 7^{5} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$0.304926699$	$1$		$13$	$3010560$	$3.243725$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.16045$	$[0, 1, 0, -17132449, 43496608991]$	\(y^2=x^3+x^2-17132449x+43496608991\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(7925, 636804)]$
44688.co2	44688bh2	44688.co	44688bh	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{11} \cdot 3^{14} \cdot 7^{11} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$18063360$	$3.870106$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.54048$	$[0, 1, 0, -209872504, -1865231919244]$	\(y^2=x^3+x^2-209872504x-1865231919244\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
60648.q2	60648w2	60648.q	60648w	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{11} \cdot 3^{14} \cdot 7^{5} \cdot 19^{12} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$89.14324141$	$1$		$1$	$67737600$	$4.369370$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.90313$	$[0, -1, 0, -1546203552, 37298316846060]$	\(y^2=x^3-x^2-1546203552x+37298316846060\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(327968793283658159547455409634922416405/104538393220872409, 4836659103592449506825991822933584881242770610338933332620/104538393220872409)]$
67032.ck2	67032cf2	67032.ck	67032cf	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( - 2^{11} \cdot 3^{20} \cdot 7^{11} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$49$	$7$	$1$	$72253440$	$4.419411$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.89499$	$[0, 0, 0, -1888852539, -50359372967050]$	\(y^2=x^3-1888852539x-50359372967050\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
76608.eb2	76608bf2	76608.eb	76608bf	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{17} \cdot 3^{20} \cdot 7^{5} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$4$	$2$	$1$	$24084480$	$3.793034$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.14478$	$[0, 0, 0, -154192044, 1174562634800]$	\(y^2=x^3-154192044x+1174562634800\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
76608.ff2	76608fn2	76608.ff	76608fn	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{17} \cdot 3^{20} \cdot 7^{5} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$3.690938171$	$1$		$3$	$24084480$	$3.793034$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.14478$	$[0, 0, 0, -154192044, -1174562634800]$	\(y^2=x^3-154192044x-1174562634800\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(20912, 2178540)]$
79800.o2	79800bj2	79800.o	79800bj	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{11} \cdot 3^{14} \cdot 5^{6} \cdot 7^{5} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$24084480$	$3.701870$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.02564$	$[0, -1, 0, -107077808, -679688054388]$	\(y^2=x^3-x^2-107077808x-679688054388\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
121296.dj2	121296bn2	121296.dj	121296bn	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{11} \cdot 3^{14} \cdot 7^{5} \cdot 19^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$4$	$2$	$1$	$135475200$	$4.369370$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.49437$	$[0, 1, 0, -1546203552, -37298316846060]$	\(y^2=x^3+x^2-1546203552x-37298316846060\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
134064.eo2	134064ew2	134064.eo	134064ew	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( - 2^{11} \cdot 3^{20} \cdot 7^{11} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$4$	$2$	$1$	$144506880$	$4.419411$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.49018$	$[0, 0, 0, -1888852539, 50359372967050]$	\(y^2=x^3-1888852539x+50359372967050\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
159600.fl2	159600gc2	159600.fl	159600gc	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{11} \cdot 3^{14} \cdot 5^{6} \cdot 7^{5} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$48168960$	$3.701870$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$5.67701$	$[0, 1, 0, -107077808, 679688054388]$	\(y^2=x^3+x^2-107077808x+679688054388\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
178752.dv2	178752et2	178752.dv	178752et	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{17} \cdot 3^{14} \cdot 7^{11} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$99.50672070$	$1$		$1$	$144506880$	$4.216682$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.13463$	$[0, -1, 0, -839490017, -14921015863935]$	\(y^2=x^3-x^2-839490017x-14921015863935\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(151169095247730369139524509408937204057825091/64803854928758775213, 333492685008441266562962610301339022472085056491418013131714085820/64803854928758775213)]$
178752.jw2	178752ho2	178752.jw	178752ho	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{17} \cdot 3^{14} \cdot 7^{11} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$144506880$	$4.216682$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.13463$	$[0, 1, 0, -839490017, 14921015863935]$	\(y^2=x^3+x^2-839490017x+14921015863935\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
181944.k2	181944bl2	181944.k	181944bl	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{11} \cdot 3^{20} \cdot 7^{5} \cdot 19^{12} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$246.1357549$	$1$		$1$	$541900800$	$4.918678$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.82121$	$[0, 0, 0, -13915831971, -1007040639011650]$	\(y^2=x^3-13915831971x-1007040639011650\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(72700314614968594885559081193667223226988656866814997521164706822500236083333629039032062717305944662218438/280950206151152510041187930112513077985858030198071, 19427997759606169440006668821619563244468787069047053838143667963170682834895093025683902807392935374336492180167055463375385075182813439643706602757686098825078/280950206151152510041187930112513077985858030198071)]$
239400.ep2	239400ep2	239400.ep	239400ep	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{11} \cdot 3^{20} \cdot 5^{6} \cdot 7^{5} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$192675840$	$4.251175$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.02336$	$[0, 0, 0, -963700275, 18352541168750]$	\(y^2=x^3-963700275x+18352541168750\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
363888.n2	363888n2	363888.n	363888n	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{11} \cdot 3^{20} \cdot 7^{5} \cdot 19^{12} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$10.19027116$	$1$		$13$	$1083801600$	$4.918678$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.45196$	$[0, 0, 0, -13915831971, 1007040639011650]$	\(y^2=x^3-13915831971x+1007040639011650\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(229463, 99477882), (-137953, 17360406)]$
386232.cc2	386232cc2	386232.cc	386232cc	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( - 2^{11} \cdot 3^{14} \cdot 7^{5} \cdot 11^{6} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$5.574843326$	$1$		$3$	$203212800$	$4.096100$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$5.65475$	$[0, 1, 0, -518256592, 7237525705760]$	\(y^2=x^3+x^2-518256592x+7237525705760\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(55055, 12065760)]$
424536.cs2	424536cs2	424536.cs	424536cs	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( - 2^{11} \cdot 3^{14} \cdot 7^{11} \cdot 19^{12} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$20.84369021$	$1$		$1$	$3251404800$	$5.342323$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.76751$	$[0, 1, 0, -75763974064, -12793171150250464]$	\(y^2=x^3+x^2-75763974064x-12793171150250464\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(353191560131/599, 200057009702149698/599)]$
478800.f2	478800f2	478800.f	478800f	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{11} \cdot 3^{20} \cdot 5^{6} \cdot 7^{5} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$385351680$	$4.251175$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$5.70414$	$[0, 0, 0, -963700275, -18352541168750]$	\(y^2=x^3-963700275x-18352541168750\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
485184.s2	485184s2	485184.s	485184s	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{17} \cdot 3^{14} \cdot 7^{5} \cdot 19^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$1083801600$	$4.715942$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.12437$	$[0, -1, 0, -6184814209, -298380349954271]$	\(y^2=x^3-x^2-6184814209x-298380349954271\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[ ]$
485184.fo2	485184fo2	485184.fo	485184fo	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{17} \cdot 3^{14} \cdot 7^{5} \cdot 19^{12} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$8.287130823$	$1$		$3$	$1083801600$	$4.715942$	$-4242991426585187031506/3781894171664380023$	$1.07701$	$6.12437$	$[0, 1, 0, -6184814209, 298380349954271]$	\(y^2=x^3+x^2-6184814209x+298380349954271\)	2.3.0.a.1, 56.6.0.b.1, 228.6.0.?, 3192.12.0.?	$[(53426, 10974933)]$

  Download displayed columns for results to