Elliptic curves over $\Q$ of conductor 8001

Results (10 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
8001.a1	8001c1	8001.a	8001c	$1$	$1$	\( 3^{2} \cdot 7 \cdot 127 \)	\( 3^{11} \cdot 7^{4} \cdot 127 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$762$	$2$	$0$	$0.325803856$	$1$		$20$	$32000$	$1.201025$	$5396947461517312/74097261$	$0.94542$	$4.76408$	$[0, 0, 1, -32889, 2295720]$	\(y^2+y=x^3-32889x+2295720\)	762.2.0.?	$[(107, 40), (92, 220)]$
8001.b1	8001b1	8001.b	8001b	$1$	$1$	\( 3^{2} \cdot 7 \cdot 127 \)	\( 3^{3} \cdot 7^{2} \cdot 127 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$762$	$2$	$0$	$0.230432249$	$1$		$16$	$1216$	$-0.232855$	$147197952/6223$	$0.73150$	$2.45937$	$[0, 0, 1, -33, 70]$	\(y^2+y=x^3-33x+70\)	762.2.0.?	$[(2, 3), (-5, 10)]$
8001.c1	8001g2	8001.c	8001g	$2$	$3$	\( 3^{2} \cdot 7 \cdot 127 \)	\( 3^{7} \cdot 7^{2} \cdot 127^{3} \)	$2$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$762$	$16$	$0$	$1.879612295$	$1$		$18$	$24192$	$1.441051$	$188692544389906432/301112301$	$1.02358$	$5.15955$	$[0, 0, 1, -107544, 13574592]$	\(y^2+y=x^3-107544x+13574592\)	3.8.0-3.a.1.2, 762.16.0.?	$[(188, 31), (1970, 86296)]$
8001.c2	8001g1	8001.c	8001g	$2$	$3$	\( 3^{2} \cdot 7 \cdot 127 \)	\( 3^{9} \cdot 7^{6} \cdot 127 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$762$	$16$	$0$	$0.208845810$	$1$		$18$	$8064$	$0.891747$	$750593769472/403418421$	$1.00298$	$3.77596$	$[0, 0, 1, -1704, 7227]$	\(y^2+y=x^3-1704x+7227\)	3.8.0-3.a.1.1, 762.16.0.?	$[(-1, 94), (185/2, 1319/2)]$
8001.d1	8001d2	8001.d	8001d	$2$	$2$	\( 3^{2} \cdot 7 \cdot 127 \)	\( 3^{18} \cdot 7^{2} \cdot 127 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3556$	$12$	$0$	$2.961375747$	$1$		$2$	$18432$	$1.098196$	$20591101178929/3307157343$	$0.90255$	$4.14446$	$[1, -1, 0, -5139, -119246]$	\(y^2+xy=x^3-x^2-5139x-119246\)	2.3.0.a.1, 28.6.0.c.1, 508.6.0.?, 3556.12.0.?	$[(-46, 158)]$
8001.d2	8001d1	8001.d	8001d	$2$	$2$	\( 3^{2} \cdot 7 \cdot 127 \)	\( - 3^{12} \cdot 7 \cdot 127^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3556$	$12$	$0$	$5.922751494$	$1$		$1$	$9216$	$0.751623$	$28962726911/82306287$	$0.87534$	$3.56554$	$[1, -1, 0, 576, -10661]$	\(y^2+xy=x^3-x^2+576x-10661\)	2.3.0.a.1, 14.6.0.b.1, 508.6.0.?, 3556.12.0.?	$[(674/5, 17647/5)]$
8001.e1	8001f2	8001.e	8001f	$2$	$2$	\( 3^{2} \cdot 7 \cdot 127 \)	\( 3^{10} \cdot 7^{6} \cdot 127 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3556$	$12$	$0$	$1.559545503$	$1$		$4$	$7680$	$1.052639$	$25477066140625/1210255263$	$0.94534$	$4.16815$	$[1, -1, 0, -5517, -149742]$	\(y^2+xy=x^3-x^2-5517x-149742\)	2.3.0.a.1, 28.6.0.c.1, 508.6.0.?, 3556.12.0.?	$[(-42, 102)]$
8001.e2	8001f1	8001.e	8001f	$2$	$2$	\( 3^{2} \cdot 7 \cdot 127 \)	\( - 3^{8} \cdot 7^{3} \cdot 127^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3556$	$12$	$0$	$3.119091006$	$1$		$3$	$3840$	$0.706066$	$1174241375/49790223$	$0.89521$	$3.53342$	$[1, -1, 0, 198, -9153]$	\(y^2+xy=x^3-x^2+198x-9153\)	2.3.0.a.1, 14.6.0.b.1, 508.6.0.?, 3556.12.0.?	$[(54, 369)]$
8001.f1	8001e1	8001.f	8001e	$1$	$1$	\( 3^{2} \cdot 7 \cdot 127 \)	\( - 3^{7} \cdot 7 \cdot 127 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$5334$	$2$	$0$	$2.110899471$	$1$		$0$	$1152$	$-0.111145$	$512000/2667$	$0.71127$	$2.42757$	$[0, 0, 1, 15, 63]$	\(y^2+y=x^3+15x+63\)	5334.2.0.?	$[(-7/2, 41/2)]$
8001.g1	8001a1	8001.g	8001a	$1$	$1$	\( 3^{2} \cdot 7 \cdot 127 \)	\( 3^{9} \cdot 7^{2} \cdot 127 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$762$	$2$	$0$	$1$	$1$		$0$	$3648$	$0.316452$	$147197952/6223$	$0.73150$	$3.19281$	$[0, 0, 1, -297, -1897]$	\(y^2+y=x^3-297x-1897\)	762.2.0.?	$[]$