Elliptic curves over $\Q$ of conductor 6321

Results (13 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
6321.a1	6321d2	6321.a	6321d	$2$	$2$	\( 3 \cdot 7^{2} \cdot 43 \)	\( 3^{12} \cdot 7^{9} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1204$	$12$	$0$	$8.674821566$	$1$		$0$	$48384$	$1.661079$	$1086056947639/22851963$	$0.93620$	$5.16781$	$[1, 1, 1, -73452, -7552224]$	\(y^2+xy+y=x^3+x^2-73452x-7552224\)	2.3.0.a.1, 28.6.0.c.1, 172.6.0.?, 602.6.0.?, 1204.12.0.?	$[(4447/3, 230386/3)]$
6321.a2	6321d1	6321.a	6321d	$2$	$2$	\( 3 \cdot 7^{2} \cdot 43 \)	\( - 3^{6} \cdot 7^{9} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1204$	$12$	$0$	$4.337410783$	$1$		$3$	$24192$	$1.314507$	$68921/1347921$	$1.02592$	$4.46568$	$[1, 1, 1, 293, -354712]$	\(y^2+xy+y=x^3+x^2+293x-354712\)	2.3.0.a.1, 14.6.0.b.1, 172.6.0.?, 1204.12.0.?	$[(456, 9511)]$
6321.b1	6321f2	6321.b	6321f	$2$	$2$	\( 3 \cdot 7^{2} \cdot 43 \)	\( 3^{12} \cdot 7^{3} \cdot 43 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1204$	$12$	$0$	$0.462750696$	$1$		$24$	$6912$	$0.688124$	$1086056947639/22851963$	$0.93620$	$3.83372$	$[1, 0, 0, -1499, 21804]$	\(y^2+xy=x^3-1499x+21804\)	2.3.0.a.1, 28.6.0.c.1, 172.6.0.?, 602.6.0.?, 1204.12.0.?	$[(4, 124), (13, 61)]$
6321.b2	6321f1	6321.b	6321f	$2$	$2$	\( 3 \cdot 7^{2} \cdot 43 \)	\( - 3^{6} \cdot 7^{3} \cdot 43^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1204$	$12$	$0$	$0.462750696$	$1$		$23$	$3456$	$0.341550$	$68921/1347921$	$1.02592$	$3.13159$	$[1, 0, 0, 6, 1035]$	\(y^2+xy=x^3+6x+1035\)	2.3.0.a.1, 14.6.0.b.1, 172.6.0.?, 1204.12.0.?	$[(-3, 33), (18, 75)]$
6321.c1	6321c3	6321.c	6321c	$3$	$9$	\( 3 \cdot 7^{2} \cdot 43 \)	\( - 3^{2} \cdot 7^{8} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$5418$	$144$	$3$	$2.297327698$	$1$		$0$	$393984$	$3.036125$	$-50096759460260217094144000/18963$	$1.10297$	$8.09580$	$[0, -1, 1, -376320653, 2809988757554]$	\(y^2+y=x^3-x^2-376320653x+2809988757554\)	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.2, 63.24.0-9.a.1.2, 86.2.0.?, $\ldots$	$[(44813/2, 4259/2)]$
6321.c2	6321c2	6321.c	6321c	$3$	$9$	\( 3 \cdot 7^{2} \cdot 43 \)	\( - 3^{6} \cdot 7^{12} \cdot 43^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$5418$	$144$	$3$	$0.765775899$	$1$		$4$	$131328$	$2.486820$	$-94260981564964864000/6819006982347$	$1.07557$	$6.58942$	$[0, -1, 1, -4645853, 3856096985]$	\(y^2+y=x^3-x^2-4645853x+3856096985\)	3.12.0.a.1, 21.24.0-3.a.1.1, 86.2.0.?, 258.24.1.?, 1806.48.1.?, $\ldots$	$[(1685, 28444)]$
6321.c3	6321c1	6321.c	6321c	$3$	$9$	\( 3 \cdot 7^{2} \cdot 43 \)	\( - 3^{18} \cdot 7^{8} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$5418$	$144$	$3$	$2.297327698$	$1$		$0$	$43776$	$1.937513$	$-8998912000/816294970323$	$1.13644$	$5.31995$	$[0, -1, 1, -2123, 14910692]$	\(y^2+y=x^3-x^2-2123x+14910692\)	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.1, 63.24.0-9.a.1.1, 86.2.0.?, $\ldots$	$[(356/5, 482171/5)]$
6321.d1	6321b1	6321.d	6321b	$1$	$1$	\( 3 \cdot 7^{2} \cdot 43 \)	\( - 3^{2} \cdot 7^{8} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$86$	$2$	$0$	$0.734541756$	$1$		$4$	$2304$	$0.483276$	$32768000/18963$	$1.44331$	$3.31143$	$[0, -1, 1, 327, -106]$	\(y^2+y=x^3-x^2+327x-106\)	86.2.0.?	$[(12, 73)]$
6321.e1	6321e1	6321.e	6321e	$1$	$1$	\( 3 \cdot 7^{2} \cdot 43 \)	\( - 3^{4} \cdot 7^{6} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$86$	$2$	$0$	$1.239610286$	$1$		$4$	$2880$	$0.505841$	$-799178752/3483$	$0.95634$	$3.67726$	$[0, 1, 1, -947, -11581]$	\(y^2+y=x^3+x^2-947x-11581\)	86.2.0.?	$[(37, 73)]$
6321.f1	6321a3	6321.f	6321a	$4$	$4$	\( 3 \cdot 7^{2} \cdot 43 \)	\( 3^{12} \cdot 7^{6} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$7224$	$48$	$0$	$1$	$1$		$0$	$11520$	$1.189781$	$1616855892553/22851963$	$1.05806$	$4.54623$	$[1, 1, 0, -11981, -503586]$	\(y^2+xy=x^3+x^2-11981x-503586\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 28.12.0-4.c.1.2, 168.24.0.?, $\ldots$	$[]$
6321.f2	6321a2	6321.f	6321a	$4$	$4$	\( 3 \cdot 7^{2} \cdot 43 \)	\( 3^{6} \cdot 7^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3612$	$48$	$0$	$1$	$1$		$2$	$5760$	$0.843208$	$2845178713/1347921$	$0.95310$	$3.82150$	$[1, 1, 0, -1446, 8415]$	\(y^2+xy=x^3+x^2-1446x+8415\)	2.6.0.a.1, 12.12.0.b.1, 28.12.0-2.a.1.1, 84.24.0.?, 172.12.0.?, $\ldots$	$[]$
6321.f3	6321a1	6321.f	6321a	$4$	$4$	\( 3 \cdot 7^{2} \cdot 43 \)	\( 3^{3} \cdot 7^{6} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$7224$	$48$	$0$	$1$	$1$		$1$	$2880$	$0.496635$	$1630532233/1161$	$0.91317$	$3.75789$	$[1, 1, 0, -1201, 15520]$	\(y^2+xy=x^3+x^2-1201x+15520\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 56.12.0-4.c.1.5, 84.12.0.?, $\ldots$	$[]$
6321.f4	6321a4	6321.f	6321a	$4$	$4$	\( 3 \cdot 7^{2} \cdot 43 \)	\( - 3^{3} \cdot 7^{6} \cdot 43^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$7224$	$48$	$0$	$1$	$1$		$0$	$11520$	$1.189781$	$129784785047/92307627$	$0.98681$	$4.25802$	$[1, 1, 0, 5169, 70596]$	\(y^2+xy=x^3+x^2+5169x+70596\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 12.12.0.g.1, 28.12.0-4.c.1.1, $\ldots$	$[]$