Elliptic curve search results

Results (29 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
1122.i2	1122i2	1122.i	1122i	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 17 \)	\( - 2^{7} \cdot 3^{10} \cdot 11^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$4488$	$12$	$0$	$0.061869181$	$1$		$22$	$2240$	$0.871135$	$-2035346265217/264305213568$	$1.01228$	$4.80709$	$[1, 0, 0, -264, 24768]$	\(y^2+xy=x^3-264x+24768\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(6, 150)]$
3366.i2	3366k2	3366.i	3366k	$2$	$2$	\( 2 \cdot 3^{2} \cdot 11 \cdot 17 \)	\( - 2^{7} \cdot 3^{16} \cdot 11^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$0$	$17920$	$1.420441$	$-2035346265217/264305213568$	$1.01228$	$4.96846$	$[1, -1, 0, -2376, -668736]$	\(y^2+xy=x^3-x^2-2376x-668736\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
8976.g2	8976u2	8976.g	8976u	$2$	$2$	\( 2^{4} \cdot 3 \cdot 11 \cdot 17 \)	\( - 2^{19} \cdot 3^{10} \cdot 11^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$4.213506324$	$1$		$3$	$53760$	$1.564281$	$-2035346265217/264305213568$	$1.01228$	$4.62271$	$[0, -1, 0, -4224, -1585152]$	\(y^2=x^3-x^2-4224x-1585152\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(197, 2278)]$
12342.j2	12342q2	12342.j	12342q	$2$	$2$	\( 2 \cdot 3 \cdot 11^{2} \cdot 17 \)	\( - 2^{7} \cdot 3^{10} \cdot 11^{8} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$0$	$268800$	$2.070084$	$-2035346265217/264305213568$	$1.01228$	$5.11072$	$[1, 0, 1, -31947, -32998154]$	\(y^2+xy+y=x^3-31947x-32998154\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
19074.w2	19074t2	19074.w	19074t	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 17^{2} \)	\( - 2^{7} \cdot 3^{10} \cdot 11^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1.530887677$	$1$		$6$	$645120$	$2.287743$	$-2035346265217/264305213568$	$1.01228$	$5.15000$	$[1, 1, 1, -76302, 121761483]$	\(y^2+xy+y=x^3+x^2-76302x+121761483\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(121, 10631)]$
26928.bw2	26928bj2	26928.bw	26928bj	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 11 \cdot 17 \)	\( - 2^{19} \cdot 3^{16} \cdot 11^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$430080$	$2.113586$	$-2035346265217/264305213568$	$1.01228$	$4.77104$	$[0, 0, 0, -38019, 42837122]$	\(y^2=x^3-38019x+42837122\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
28050.u2	28050i2	28050.u	28050i	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 \)	\( - 2^{7} \cdot 3^{10} \cdot 5^{6} \cdot 11^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$0$	$286720$	$1.675854$	$-2035346265217/264305213568$	$1.01228$	$4.23914$	$[1, 1, 0, -6600, 3096000]$	\(y^2+xy=x^3+x^2-6600x+3096000\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
35904.ba2	35904q2	35904.ba	35904q	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11 \cdot 17 \)	\( - 2^{25} \cdot 3^{10} \cdot 11^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$430080$	$1.910854$	$-2035346265217/264305213568$	$1.01228$	$4.40823$	$[0, -1, 0, -16897, 12698113]$	\(y^2=x^3-x^2-16897x+12698113\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
35904.de2	35904ck2	35904.de	35904ck	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11 \cdot 17 \)	\( - 2^{25} \cdot 3^{10} \cdot 11^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$3.066121533$	$1$		$5$	$430080$	$1.910854$	$-2035346265217/264305213568$	$1.01228$	$4.40823$	$[0, 1, 0, -16897, -12698113]$	\(y^2=x^3+x^2-16897x-12698113\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(554, 12177)]$
37026.bp2	37026bd2	37026.bp	37026bd	$2$	$2$	\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 17 \)	\( - 2^{7} \cdot 3^{16} \cdot 11^{8} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$0$	$2150400$	$2.619389$	$-2035346265217/264305213568$	$1.01228$	$5.20360$	$[1, -1, 1, -287519, 890950151]$	\(y^2+xy+y=x^3-x^2-287519x+890950151\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
54978.bs2	54978bo2	54978.bs	54978bo	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 \)	\( - 2^{7} \cdot 3^{10} \cdot 7^{6} \cdot 11^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$0$	$645120$	$1.844090$	$-2035346265217/264305213568$	$1.01228$	$4.16274$	$[1, 1, 1, -12937, -8508361]$	\(y^2+xy+y=x^3+x^2-12937x-8508361\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
57222.i2	57222k2	57222.i	57222k	$2$	$2$	\( 2 \cdot 3^{2} \cdot 11 \cdot 17^{2} \)	\( - 2^{7} \cdot 3^{16} \cdot 11^{2} \cdot 17^{8} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$15.06160558$	$1$		$8$	$5160960$	$2.837048$	$-2035346265217/264305213568$	$1.01228$	$5.23524$	$[1, -1, 0, -686718, -3288246764]$	\(y^2+xy=x^3-x^2-686718x-3288246764\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(4739, 313652), (24815, 3893984)]$
84150.hc2	84150fr2	84150.hc	84150fr	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 \)	\( - 2^{7} \cdot 3^{16} \cdot 5^{6} \cdot 11^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$0$	$2293760$	$2.225159$	$-2035346265217/264305213568$	$1.01228$	$4.40972$	$[1, -1, 1, -59405, -83651403]$	\(y^2+xy+y=x^3-x^2-59405x-83651403\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
98736.g2	98736cr2	98736.g	98736cr	$2$	$2$	\( 2^{4} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( - 2^{19} \cdot 3^{10} \cdot 11^{8} \cdot 17^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$3.923413620$	$1$		$17$	$6451200$	$2.763229$	$-2035346265217/264305213568$	$1.01228$	$4.90988$	$[0, -1, 0, -511144, 2111881840]$	\(y^2=x^3-x^2-511144x+2111881840\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(642, 45254), (772, 46656)]$
107712.l2	107712bs2	107712.l	107712bs	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 \)	\( - 2^{25} \cdot 3^{16} \cdot 11^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$7.075294661$	$1$		$3$	$3440640$	$2.460163$	$-2035346265217/264305213568$	$1.01228$	$4.55915$	$[0, 0, 0, -152076, -342696976]$	\(y^2=x^3-152076x-342696976\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(23080, 3505788)]$
107712.bs2	107712ff2	107712.bs	107712ff	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 \)	\( - 2^{25} \cdot 3^{16} \cdot 11^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$2.638821689$	$1$		$3$	$3440640$	$2.460163$	$-2035346265217/264305213568$	$1.01228$	$4.55915$	$[0, 0, 0, -152076, 342696976]$	\(y^2=x^3-152076x+342696976\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(4226, 274176)]$
152592.ct2	152592w2	152592.ct	152592w	$2$	$2$	\( 2^{4} \cdot 3 \cdot 11 \cdot 17^{2} \)	\( - 2^{19} \cdot 3^{10} \cdot 11^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$4.071539963$	$1$		$5$	$15482880$	$2.980888$	$-2035346265217/264305213568$	$1.01228$	$4.94964$	$[0, 1, 0, -1220832, -7795176588]$	\(y^2=x^3+x^2-1220832x-7795176588\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(2484, 67122)]$
164934.r2	164934cw2	164934.r	164934cw	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \cdot 17 \)	\( - 2^{7} \cdot 3^{16} \cdot 7^{6} \cdot 11^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$0$	$5160960$	$2.393394$	$-2035346265217/264305213568$	$1.01228$	$4.33076$	$[1, -1, 0, -116433, 229609309]$	\(y^2+xy=x^3-x^2-116433x+229609309\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
189618.u2	189618be2	189618.u	189618be	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13^{2} \cdot 17 \)	\( - 2^{7} \cdot 3^{10} \cdot 11^{2} \cdot 13^{6} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$2.361402797$	$1$		$4$	$4838400$	$2.153610$	$-2035346265217/264305213568$	$1.01228$	$4.04428$	$[1, 0, 1, -44620, 54459914]$	\(y^2+xy+y=x^3-44620x+54459914\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(-74, 7610)]$
209814.r2	209814cz2	209814.r	209814cz	$2$	$2$	\( 2 \cdot 3 \cdot 11^{2} \cdot 17^{2} \)	\( - 2^{7} \cdot 3^{10} \cdot 11^{8} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$4$	$2$	$0$	$77414400$	$3.486687$	$-2035346265217/264305213568$	$1.01228$	$5.31633$	$[1, 1, 0, -9232544, -162110696832]$	\(y^2+xy=x^3+x^2-9232544x-162110696832\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
224400.ex2	224400be2	224400.ex	224400be	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 \)	\( - 2^{19} \cdot 3^{10} \cdot 5^{6} \cdot 11^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1.132152309$	$1$		$9$	$6881280$	$2.368999$	$-2035346265217/264305213568$	$1.01228$	$4.19878$	$[0, 1, 0, -105608, -198355212]$	\(y^2=x^3+x^2-105608x-198355212\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(1918, 81600)]$
296208.eg2	296208eg2	296208.eg	296208eg	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 \)	\( - 2^{19} \cdot 3^{16} \cdot 11^{8} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$51609600$	$3.312534$	$-2035346265217/264305213568$	$1.01228$	$5.00494$	$[0, 0, 0, -4600299, -57016209382]$	\(y^2=x^3-4600299x-57016209382\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
308550.fh2	308550fh2	308550.fh	308550fh	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 17 \)	\( - 2^{7} \cdot 3^{10} \cdot 5^{6} \cdot 11^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$2.404398218$	$1$		$4$	$34406400$	$2.874802$	$-2035346265217/264305213568$	$1.01228$	$4.57320$	$[1, 1, 1, -798663, -4124769219]$	\(y^2+xy+y=x^3+x^2-798663x-4124769219\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(2525, 98562)]$
394944.ec2	394944ec2	394944.ec	394944ec	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( - 2^{25} \cdot 3^{10} \cdot 11^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$24.91215060$	$1$		$1$	$51609600$	$3.109802$	$-2035346265217/264305213568$	$1.01228$	$4.70442$	$[0, -1, 0, -2044577, -16893010143]$	\(y^2=x^3-x^2-2044577x-16893010143\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(21135564109223/29741, 96930986822741092032/29741)]$
394944.ia2	394944ia2	394944.ia	394944ia	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( - 2^{25} \cdot 3^{10} \cdot 11^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1.382788675$	$1$		$7$	$51609600$	$3.109802$	$-2035346265217/264305213568$	$1.01228$	$4.70442$	$[0, 1, 0, -2044577, 16893010143]$	\(y^2=x^3+x^2-2044577x+16893010143\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(-1913, 117504)]$
405042.g2	405042g2	405042.g	405042g	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 17 \cdot 19^{2} \)	\( - 2^{7} \cdot 3^{10} \cdot 11^{2} \cdot 17^{2} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$0$	$13547520$	$2.343353$	$-2035346265217/264305213568$	$1.01228$	$3.98290$	$[1, 1, 0, -95311, -170074331]$	\(y^2+xy=x^3+x^2-95311x-170074331\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
439824.gb2	439824gb2	439824.gb	439824gb	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 \)	\( - 2^{19} \cdot 3^{10} \cdot 7^{6} \cdot 11^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$15482880$	$2.537235$	$-2035346265217/264305213568$	$1.01228$	$4.13670$	$[0, 1, 0, -206992, 544121108]$	\(y^2=x^3+x^2-206992x+544121108\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
457776.u2	457776u2	457776.u	457776u	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 11 \cdot 17^{2} \)	\( - 2^{19} \cdot 3^{16} \cdot 11^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$123863040$	$3.530193$	$-2035346265217/264305213568$	$1.01228$	$5.03818$	$[0, 0, 0, -10987491, 210458780386]$	\(y^2=x^3-10987491x+210458780386\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[]$
476850.df2	476850df2	476850.df	476850df	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17^{2} \)	\( - 2^{7} \cdot 3^{10} \cdot 5^{6} \cdot 11^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$4488$	$12$	$0$	$1.647138977$	$1$		$6$	$82575360$	$3.092461$	$-2035346265217/264305213568$	$1.01228$	$4.62070$	$[1, 0, 1, -1907551, 15224000498]$	\(y^2+xy+y=x^3-1907551x+15224000498\)	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(772, 118826)]$