Elliptic curve search results

Results (27 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
2310.c4	2310c4	2310.c	2310c	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{3} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$264$	$48$	$0$	$1.096677767$	$1$		$6$	$6144$	$1.150806$	$11456208593737991/6725709375000$	$1.01509$	$4.77434$	$[1, 1, 0, 4697, -12947]$	\(y^2+xy=x^3+x^2+4697x-12947\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 12.12.0-4.c.1.1, 24.24.0-24.v.1.4, $\ldots$	$[(33, 407)]$
6930.bf4	6930bi4	6930.bf	6930bi	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{3} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$264$	$48$	$0$	$0.506442628$	$1$		$8$	$49152$	$1.700111$	$11456208593737991/6725709375000$	$1.01509$	$4.92660$	$[1, -1, 1, 42268, 391839]$	\(y^2+xy+y=x^3-x^2+42268x+391839\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.v.1.1, 88.24.0.?, 264.48.0.?	$[(47, 1551)]$
11550.cl4	11550ci4	11550.cl	11550ci	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{3} \cdot 3 \cdot 5^{14} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1$	$1$		$0$	$147456$	$1.955524$	$11456208593737991/6725709375000$	$1.01509$	$4.98522$	$[1, 0, 0, 117412, -1853208]$	\(y^2+xy=x^3+117412x-1853208\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 40.12.0-4.c.1.1, 60.12.0-4.c.1.1, $\ldots$	$[ ]$
16170.bh4	16170bf4	16170.bh	16170bf	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{3} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$0.909801723$	$1$		$4$	$294912$	$2.123760$	$11456208593737991/6725709375000$	$1.01509$	$5.02045$	$[1, 0, 1, 230127, 5131228]$	\(y^2+xy+y=x^3+230127x+5131228\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 56.12.0-4.c.1.2, 84.12.0.?, $\ldots$	$[(844, 27875)]$
18480.bt4	18480cn4	18480.bt	18480cn	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{15} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$264$	$48$	$0$	$5.814642649$	$1$		$1$	$147456$	$1.843952$	$11456208593737991/6725709375000$	$1.01509$	$4.61045$	$[0, 1, 0, 75144, 978900]$	\(y^2=x^3+x^2+75144x+978900\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.2, 24.24.0-24.v.1.3, $\ldots$	$[(764/5, 227238/5)]$
25410.bn4	25410bm3	25410.bn	25410bm	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$264$	$48$	$0$	$3.829500672$	$1$		$2$	$737280$	$2.349754$	$11456208593737991/6725709375000$	$1.01509$	$5.06410$	$[1, 1, 1, 568274, 20073923]$	\(y^2+xy+y=x^3+x^2+568274x+20073923\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 24.24.0-24.v.1.6, 88.24.0.?, $\ldots$	$[(1371, 57439)]$
34650.h4	34650m3	34650.h	34650m	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{3} \cdot 3^{7} \cdot 5^{14} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1$	$1$		$0$	$1179648$	$2.504829$	$11456208593737991/6725709375000$	$1.01509$	$5.09187$	$[1, -1, 0, 1056708, 50036616]$	\(y^2+xy=x^3-x^2+1056708x+50036616\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0.v.1, 88.12.0.?, $\ldots$	$[ ]$
48510.cp4	48510da3	48510.cp	48510da	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{3} \cdot 3^{7} \cdot 5^{8} \cdot 7^{8} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$1$		$0$	$2359296$	$2.673069$	$11456208593737991/6725709375000$	$1.01509$	$5.12019$	$[1, -1, 1, 2071147, -138543163]$	\(y^2+xy+y=x^3-x^2+2071147x-138543163\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 28.12.0-4.c.1.1, 88.12.0.?, $\ldots$	$[ ]$
55440.dh4	55440ej3	55440.dh	55440ej	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{15} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$264$	$48$	$0$	$0.663418495$	$1$		$19$	$1179648$	$2.393261$	$11456208593737991/6725709375000$	$1.01509$	$4.75020$	$[0, 0, 0, 676293, -25754006]$	\(y^2=x^3+676293x-25754006\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.v.1.2, 88.24.0.?, 264.48.0.?	$[(93, 6160)]$
73920.de4	73920fo3	73920.de	73920fo	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{21} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$264$	$48$	$0$	$1$	$1$		$3$	$1179648$	$2.190525$	$11456208593737991/6725709375000$	$1.01509$	$4.41130$	$[0, -1, 0, 300575, 7530625]$	\(y^2=x^3-x^2+300575x+7530625\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.v.1.2, 88.24.0.?, 264.48.0.?	$[ ]$
73920.hy4	73920do3	73920.hy	73920do	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{21} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$264$	$48$	$0$	$1$	$1$		$1$	$1179648$	$2.190525$	$11456208593737991/6725709375000$	$1.01509$	$4.41130$	$[0, 1, 0, 300575, -7530625]$	\(y^2=x^3+x^2+300575x-7530625\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.v.1.1, 88.24.0.?, 264.48.0.?	$[ ]$
76230.bz4	76230by3	76230.bz	76230by	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 11^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.13	2B	$264$	$48$	$0$	$1$	$1$		$0$	$5898240$	$2.899059$	$11456208593737991/6725709375000$	$1.01509$	$5.15557$	$[1, -1, 0, 5114466, -536881460]$	\(y^2+xy=x^3-x^2+5114466x-536881460\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.6, 24.24.0-24.v.1.8, 44.12.0-4.c.1.1, $\ldots$	$[ ]$
80850.ei4	80850ev3	80850.ei	80850ev	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 2^{3} \cdot 3 \cdot 5^{14} \cdot 7^{8} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$0$	$7077888$	$2.928478$	$11456208593737991/6725709375000$	$1.01509$	$5.15996$	$[1, 1, 1, 5753187, 641403531]$	\(y^2+xy+y=x^3+x^2+5753187x+641403531\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 88.12.0.?, 264.24.0.?, $\ldots$	$[ ]$
92400.cr4	92400eh3	92400.cr	92400eh	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{15} \cdot 3 \cdot 5^{14} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$3.557840170$	$1$		$3$	$3538944$	$2.648670$	$11456208593737991/6725709375000$	$1.01509$	$4.80604$	$[0, -1, 0, 1878592, 118605312]$	\(y^2=x^3-x^2+1878592x+118605312\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 40.12.0-4.c.1.2, 60.12.0-4.c.1.2, $\ldots$	$[(1026, 55902)]$
127050.dt4	127050dq3	127050.dt	127050dq	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 3 \cdot 5^{14} \cdot 7^{2} \cdot 11^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1$	$4$	$2$	$0$	$17694720$	$3.154472$	$11456208593737991/6725709375000$	$1.01509$	$5.19227$	$[1, 0, 1, 14206849, 2480826698]$	\(y^2+xy+y=x^3+14206849x+2480826698\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 40.12.0-4.c.1.5, 88.12.0.?, $\ldots$	$[ ]$
129360.cv4	129360fd3	129360.cv	129360fd	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{15} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$7077888$	$2.816910$	$11456208593737991/6725709375000$	$1.01509$	$4.84017$	$[0, -1, 0, 3682040, -328398608]$	\(y^2=x^3-x^2+3682040x-328398608\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 56.12.0-4.c.1.1, 84.12.0.?, $\ldots$	$[ ]$
177870.hv4	177870b4	177870.hv	177870b	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{3} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 11^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$1$		$0$	$35389440$	$3.322708$	$11456208593737991/6725709375000$	$1.01509$	$5.21475$	$[1, 0, 0, 27845425, -6801819375]$	\(y^2+xy=x^3+27845425x-6801819375\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 56.12.0-4.c.1.5, 88.12.0.?, $\ldots$	$[ ]$
203280.fj4	203280bn4	203280.fj	203280bn	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{15} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$264$	$48$	$0$	$9.044279156$	$1$		$1$	$17694720$	$3.042900$	$11456208593737991/6725709375000$	$1.01509$	$4.88306$	$[0, 1, 0, 9092384, -1266546316]$	\(y^2=x^3+x^2+9092384x-1266546316\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 24.24.0-24.v.1.6, 88.24.0.?, $\ldots$	$[(113491/13, 157552500/13)]$
221760.bq4	221760fo4	221760.bq	221760fo	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{21} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$264$	$48$	$0$	$8.421350999$	$1$		$1$	$9437184$	$2.739834$	$11456208593737991/6725709375000$	$1.01509$	$4.55309$	$[0, 0, 0, 2705172, -206032048]$	\(y^2=x^3+2705172x-206032048\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.2, 24.24.0-24.v.1.3, $\ldots$	$[(106309/3, 34994375/3)]$
221760.gn4	221760kq3	221760.gn	221760kq	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{21} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$264$	$48$	$0$	$1$	$1$		$1$	$9437184$	$2.739834$	$11456208593737991/6725709375000$	$1.01509$	$4.55309$	$[0, 0, 0, 2705172, 206032048]$	\(y^2=x^3+2705172x+206032048\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 12.12.0-4.c.1.1, 24.24.0-24.v.1.4, $\ldots$	$[ ]$
242550.a4	242550a4	242550.a	242550a	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 2^{3} \cdot 3^{7} \cdot 5^{14} \cdot 7^{8} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$4.647998901$	$1$		$4$	$56623104$	$3.477787$	$11456208593737991/6725709375000$	$1.01509$	$5.23439$	$[1, -1, 0, 51778683, -17266116659]$	\(y^2+xy=x^3-x^2+51778683x-17266116659\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 88.12.0.?, 140.12.0.?, $\ldots$	$[(1815, 286649)]$
277200.nw4	277200nw4	277200.nw	277200nw	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{15} \cdot 3^{7} \cdot 5^{14} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$5.757472664$	$1$		$3$	$28311552$	$3.197979$	$11456208593737991/6725709375000$	$1.01509$	$4.91070$	$[0, 0, 0, 16907325, -3219250750]$	\(y^2=x^3+16907325x-3219250750\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.v.1, 88.12.0.?, $\ldots$	$[(1711, 175266)]$
369600.b4	369600b4	369600.b	369600b	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{21} \cdot 3 \cdot 5^{14} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$5.543654308$	$1$		$5$	$28311552$	$2.995247$	$11456208593737991/6725709375000$	$1.01509$	$4.61075$	$[0, -1, 0, 7514367, -956356863]$	\(y^2=x^3-x^2+7514367x-956356863\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0.v.1, 88.12.0.?, $\ldots$	$[(248, 30371)]$
369600.uk4	369600uk3	369600.uk	369600uk	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{21} \cdot 3 \cdot 5^{14} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$7.537000652$	$1$		$3$	$28311552$	$2.995247$	$11456208593737991/6725709375000$	$1.01509$	$4.61075$	$[0, 1, 0, 7514367, 956356863]$	\(y^2=x^3+x^2+7514367x+956356863\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.v.1, 88.12.0.?, $\ldots$	$[(3122, 234213)]$
381150.my4	381150my4	381150.my	381150my	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 3^{7} \cdot 5^{14} \cdot 7^{2} \cdot 11^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$3.256874895$	$1$		$4$	$141557760$	$3.703777$	$11456208593737991/6725709375000$	$1.01509$	$5.26132$	$[1, -1, 1, 127861645, -66982320853]$	\(y^2+xy+y=x^3-x^2+127861645x-66982320853\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 40.12.0-4.c.1.6, 88.12.0.?, $\ldots$	$[(4429, 763410)]$
388080.hn4	388080hn3	388080.hn	388080hn	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{15} \cdot 3^{7} \cdot 5^{8} \cdot 7^{8} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$2.850804554$	$1$		$3$	$56623104$	$3.366215$	$11456208593737991/6725709375000$	$1.01509$	$4.93919$	$[0, 0, 0, 33138357, 8833624058]$	\(y^2=x^3+33138357x+8833624058\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 28.12.0-4.c.1.2, 88.12.0.?, $\ldots$	$[(68341, 17929296)]$
390390.dj4	390390dj4	390390.dj	390390dj	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} \)	\( - 2^{3} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$1.979186564$	$1$		$4$	$11796480$	$2.433281$	$11456208593737991/6725709375000$	$1.01509$	$4.06737$	$[1, 1, 1, 793705, -32413243]$	\(y^2+xy+y=x^3+x^2+793705x-32413243\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[(797, 32876)]$

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