Elliptic curve search results

Results (27 matches)

 

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
1110.g1	1110f3	1110.g	1110f	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 37 \)	\( 2^{3} \cdot 3^{16} \cdot 5^{5} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$1480$	$48$	$0$	$1$	$1$		$0$	$23040$	$2.202793$	$3639478711331685826729/2016912141902025000$	$1.06074$	$7.08005$	$[1, 0, 1, -320459, -14401618]$	\(y^2+xy+y=x^3-320459x-14401618\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 20.12.0-4.c.1.1, 40.24.0-40.v.1.4, $\ldots$	$[]$
3330.ba1	3330x3	3330.ba	3330x	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 37 \)	\( 2^{3} \cdot 3^{22} \cdot 5^{5} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4440$	$48$	$0$	$1$	$1$		$0$	$184320$	$2.752098$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.93376$	$[1, -1, 1, -2884127, 388843679]$	\(y^2+xy+y=x^3-x^2-2884127x+388843679\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 40.12.0.v.1, 60.12.0-4.c.1.1, $\ldots$	$[]$
5550.w1	5550bc3	5550.w	5550bc	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{16} \cdot 5^{11} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1480$	$48$	$0$	$1.976417670$	$1$		$2$	$552960$	$3.007511$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.87843$	$[1, 1, 1, -8011463, -1800202219]$	\(y^2+xy+y=x^3+x^2-8011463x-1800202219\)	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.v.1.1, 296.24.0.?, 1480.48.0.?	$[(5105, 298072)]$
8880.a1	8880l3	8880.a	8880l	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 37 \)	\( 2^{15} \cdot 3^{16} \cdot 5^{5} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1480$	$48$	$0$	$1$	$1$		$1$	$552960$	$2.895939$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.37557$	$[0, -1, 0, -5127336, 921703536]$	\(y^2=x^3-x^2-5127336x+921703536\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 20.12.0-4.c.1.2, 40.24.0-40.v.1.2, $\ldots$	$[]$
16650.b1	16650bd3	16650.b	16650bd	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{22} \cdot 5^{11} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4440$	$48$	$0$	$5.263476983$	$1$		$2$	$4423680$	$3.556816$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.77915$	$[1, -1, 0, -72103167, 48533356741]$	\(y^2+xy=x^3-x^2-72103167x+48533356741\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.v.1, 120.24.0.?, $\ldots$	$[(113, 200909)]$
26640.bd1	26640bv4	26640.bd	26640bv	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 37 \)	\( 2^{15} \cdot 3^{22} \cdot 5^{5} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4440$	$48$	$0$	$1$	$1$		$1$	$4423680$	$3.445244$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.33508$	$[0, 0, 0, -46146027, -24839849446]$	\(y^2=x^3-46146027x-24839849446\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 40.12.0.v.1, 60.12.0-4.c.1.2, $\ldots$	$[]$
35520.bl1	35520s4	35520.bl	35520s	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 37 \)	\( 2^{21} \cdot 3^{16} \cdot 5^{5} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1480$	$48$	$0$	$1.844846235$	$1$		$3$	$4423680$	$3.242512$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.92896$	$[0, -1, 0, -20509345, -7353118943]$	\(y^2=x^3-x^2-20509345x-7353118943\)	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.v.1.1, 296.24.0.?, 1480.48.0.?	$[(-711, 82880)]$
35520.ck1	35520dd4	35520.ck	35520dd	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 37 \)	\( 2^{21} \cdot 3^{16} \cdot 5^{5} \cdot 37^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1480$	$48$	$0$	$1.044045497$	$1$		$13$	$4423680$	$3.242512$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.92896$	$[0, 1, 0, -20509345, 7353118943]$	\(y^2=x^3+x^2-20509345x+7353118943\)	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.v.1.3, 296.24.0.?, 1480.48.0.?	$[(341, 19980)]$
41070.bl1	41070bk4	41070.bl	41070bk	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 37^{2} \)	\( 2^{3} \cdot 3^{16} \cdot 5^{5} \cdot 37^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1480$	$48$	$0$	$1$	$1$		$0$	$31518720$	$4.008247$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.71293$	$[1, 0, 0, -438707715, -728169020775]$	\(y^2+xy=x^3-438707715x-728169020775\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.v.1.7, 296.24.0.?, $\ldots$	$[]$
44400.dg1	44400cv4	44400.dg	44400cv	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 37 \)	\( 2^{15} \cdot 3^{16} \cdot 5^{11} \cdot 37^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1480$	$48$	$0$	$1$	$1$		$3$	$13271040$	$3.700657$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.31909$	$[0, 1, 0, -128183408, 114956575188]$	\(y^2=x^3+x^2-128183408x+114956575188\)	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.v.1.3, 296.24.0.?, 1480.48.0.?	$[]$
54390.n1	54390k4	54390.n	54390k	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{16} \cdot 5^{5} \cdot 7^{6} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10360$	$48$	$0$	$4.943868787$	$1$		$2$	$6635520$	$3.175747$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.62380$	$[1, 1, 0, -15702467, 4924052421]$	\(y^2+xy=x^3+x^2-15702467x+4924052421\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0.v.1, 56.12.0-4.c.1.2, 140.12.0.?, $\ldots$	$[(5277, 260124)]$
106560.h1	106560fi4	106560.h	106560fi	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 37 \)	\( 2^{21} \cdot 3^{22} \cdot 5^{5} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4440$	$48$	$0$	$1$	$1$		$1$	$35389440$	$3.791817$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.93570$	$[0, 0, 0, -184584108, -198718795568]$	\(y^2=x^3-184584108x-198718795568\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.v.1, 120.24.0.?, $\ldots$	$[]$
106560.di1	106560ce4	106560.di	106560ce	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 37 \)	\( 2^{21} \cdot 3^{22} \cdot 5^{5} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4440$	$48$	$0$	$22.27815706$	$1$		$1$	$35389440$	$3.791817$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.93570$	$[0, 0, 0, -184584108, 198718795568]$	\(y^2=x^3-184584108x+198718795568\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.v.1, 120.24.0.?, $\ldots$	$[(-295697726684/4585, 10604721833360136/4585)]$
123210.w1	123210bh4	123210.w	123210bh	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 37^{2} \)	\( 2^{3} \cdot 3^{22} \cdot 5^{5} \cdot 37^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4440$	$48$	$0$	$1$	$9$	$3$	$0$	$252149760$	$4.557556$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.64611$	$[1, -1, 0, -3948369435, 19660563560925]$	\(y^2+xy=x^3-x^2-3948369435x+19660563560925\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0.v.1, 120.24.0.?, $\ldots$	$[]$
133200.gt1	133200dr4	133200.gt	133200dr	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 37 \)	\( 2^{15} \cdot 3^{22} \cdot 5^{11} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4440$	$48$	$0$	$1$	$9$	$3$	$1$	$106168320$	$4.249962$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.28938$	$[0, 0, 0, -1153650675, -3104981180750]$	\(y^2=x^3-1153650675x-3104981180750\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.v.1, 120.24.0.?, $\ldots$	$[]$
134310.ck1	134310f3	134310.ck	134310f	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{16} \cdot 5^{5} \cdot 11^{6} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$16280$	$48$	$0$	$1$	$1$		$0$	$29491200$	$3.401737$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.42293$	$[1, 0, 0, -38775481, 19129777745]$	\(y^2+xy=x^3-38775481x+19129777745\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0.v.1, 88.12.0.?, 220.12.0.?, $\ldots$	$[]$
163170.dq1	163170z4	163170.dq	163170z	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{22} \cdot 5^{5} \cdot 7^{6} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$31080$	$48$	$0$	$1$	$4$	$2$	$0$	$53084160$	$3.725052$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.65824$	$[1, -1, 1, -141322208, -133090737573]$	\(y^2+xy+y=x^3-x^2-141322208x-133090737573\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0.v.1, 168.12.0.?, 296.12.0.?, $\ldots$	$[]$
177600.eq1	177600em3	177600.eq	177600em	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 37 \)	\( 2^{21} \cdot 3^{16} \cdot 5^{11} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1480$	$48$	$0$	$1$	$25$	$5$	$1$	$106168320$	$4.047234$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.93842$	$[0, -1, 0, -512733633, 920165335137]$	\(y^2=x^3-x^2-512733633x+920165335137\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 20.12.0-4.c.1.2, 40.24.0-40.v.1.2, $\ldots$	$[]$
177600.ey1	177600fo4	177600.ey	177600fo	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 37 \)	\( 2^{21} \cdot 3^{16} \cdot 5^{11} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1480$	$48$	$0$	$1$	$1$		$1$	$106168320$	$4.047234$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.93842$	$[0, 1, 0, -512733633, -920165335137]$	\(y^2=x^3+x^2-512733633x-920165335137\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 20.12.0-4.c.1.1, 40.24.0-40.v.1.4, $\ldots$	$[]$
187590.cq1	187590a4	187590.cq	187590a	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{16} \cdot 5^{5} \cdot 13^{6} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$19240$	$48$	$0$	$0.197983094$	$1$		$10$	$53084160$	$3.485268$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.35626$	$[1, 0, 0, -54157490, -31586196708]$	\(y^2+xy=x^3-54157490x-31586196708\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0.v.1, 104.12.0.?, 260.12.0.?, $\ldots$	$[(-5966, 284368)]$
205350.d1	205350du4	205350.d	205350du	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 37^{2} \)	\( 2^{3} \cdot 3^{16} \cdot 5^{11} \cdot 37^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.13	2B	$1480$	$48$	$0$	$58.54473638$	$1$		$0$	$756449280$	$4.812973$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.61913$	$[1, 1, 0, -10967692875, -91021127596875]$	\(y^2+xy=x^3+x^2-10967692875x-91021127596875\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.6, 40.24.0-40.v.1.8, 148.12.0.?, $\ldots$	$[(-363140415729538709707875891/141569632589, 28646863395356775263090223454243978808019/141569632589)]$
271950.ih1	271950ih3	271950.ih	271950ih	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{16} \cdot 5^{11} \cdot 7^{6} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10360$	$48$	$0$	$2.457589944$	$1$		$4$	$159252480$	$3.980465$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.67219$	$[1, 0, 0, -392561688, 616291675992]$	\(y^2+xy=x^3-392561688x+616291675992\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 40.12.0.v.1, 280.24.0.?, $\ldots$	$[(-1254, 1052574)]$
320790.g1	320790g4	320790.g	320790g	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 17^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{16} \cdot 5^{5} \cdot 17^{6} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$25160$	$48$	$0$	$3.722911451$	$1$		$4$	$117964800$	$3.619396$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.25655$	$[1, 1, 0, -92612512, -70662535496]$	\(y^2+xy=x^3+x^2-92612512x-70662535496\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0.v.1, 136.12.0.?, 296.12.0.?, $\ldots$	$[(-7577, 446656)]$
328560.r1	328560r3	328560.r	328560r	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 37^{2} \)	\( 2^{15} \cdot 3^{16} \cdot 5^{5} \cdot 37^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1480$	$48$	$0$	$5.425752606$	$1$		$3$	$756449280$	$4.701401$	$3639478711331685826729/2016912141902025000$	$1.06074$	$6.26881$	$[0, -1, 0, -7019323440, 46602817329600]$	\(y^2=x^3-x^2-7019323440x+46602817329600\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.v.1.7, 296.24.0.?, $\ldots$	$[(-83784, 6823440)]$
400710.bf1	400710bf3	400710.bf	400710bf	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 19^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{16} \cdot 5^{5} \cdot 19^{6} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$28120$	$48$	$0$	$1$	$9$	$3$	$0$	$165888000$	$3.675011$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.21764$	$[1, 1, 1, -115685526, 98549325099]$	\(y^2+xy+y=x^3+x^2-115685526x+98549325099\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0.v.1, 152.12.0.?, 296.12.0.?, $\ldots$	$[]$
402930.bk1	402930bk4	402930.bk	402930bk	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 37 \)	\( 2^{3} \cdot 3^{22} \cdot 5^{5} \cdot 11^{6} \cdot 37^{4} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$48840$	$48$	$0$	$13.91617065$	$1$		$8$	$235929600$	$3.951046$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.47205$	$[1, -1, 0, -348979329, -516503999115]$	\(y^2+xy=x^3-x^2-348979329x-516503999115\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0.v.1, 264.12.0.?, 296.12.0.?, $\ldots$	$[(-3129, 739677), (-1889, 369692)]$
435120.gx1	435120gx4	435120.gx	435120gx	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 37 \)	\( 2^{15} \cdot 3^{16} \cdot 5^{5} \cdot 7^{6} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10360$	$48$	$0$	$1.543849865$	$1$		$7$	$159252480$	$3.868893$	$3639478711331685826729/2016912141902025000$	$1.06074$	$5.36373$	$[0, 1, 0, -251239480, -315641833900]$	\(y^2=x^3+x^2-251239480x-315641833900\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0.v.1, 56.12.0-4.c.1.1, 140.12.0.?, $\ldots$	$[(-2860, 616050)]$