Elliptic curves over $\Q$ of conductor 1827

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
1827.a1	1827d2	1827.a	1827d	$2$	$2$	\( 3^{2} \cdot 7 \cdot 29 \)	\( 3^{6} \cdot 7^{2} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$812$	$12$	$0$	$1$	$1$		$0$	$576$	$0.373672$	$408023180713/1421$	$0.90984$	$4.43733$	$[1, -1, 1, -1391, -19614]$	\(y^2+xy+y=x^3-x^2-1391x-19614\)	2.3.0.a.1, 28.6.0.c.1, 58.6.0.a.1, 812.12.0.?	$[]$
1827.a2	1827d1	1827.a	1827d	$2$	$2$	\( 3^{2} \cdot 7 \cdot 29 \)	\( - 3^{6} \cdot 7 \cdot 29^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$812$	$12$	$0$	$1$	$1$		$1$	$288$	$0.027098$	$-95443993/5887$	$0.82232$	$3.33763$	$[1, -1, 1, -86, -300]$	\(y^2+xy+y=x^3-x^2-86x-300\)	2.3.0.a.1, 14.6.0.b.1, 116.6.0.?, 812.12.0.?	$[]$
1827.b1	1827c2	1827.b	1827c	$2$	$2$	\( 3^{2} \cdot 7 \cdot 29 \)	\( 3^{8} \cdot 7 \cdot 29^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2436$	$12$	$0$	$0.858912670$	$1$		$6$	$512$	$0.271572$	$4956477625/52983$	$0.86867$	$3.85006$	$[1, -1, 1, -320, -2100]$	\(y^2+xy+y=x^3-x^2-320x-2100\)	2.3.0.a.1, 28.6.0.a.1, 348.6.0.?, 2436.12.0.?	$[(-10, 9)]$
1827.b2	1827c1	1827.b	1827c	$2$	$2$	\( 3^{2} \cdot 7 \cdot 29 \)	\( - 3^{7} \cdot 7^{2} \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2436$	$12$	$0$	$1.717825340$	$1$		$5$	$256$	$-0.075002$	$-15625/4263$	$0.95144$	$2.98335$	$[1, -1, 1, -5, -84]$	\(y^2+xy+y=x^3-x^2-5x-84\)	2.3.0.a.1, 28.6.0.b.1, 174.6.0.?, 2436.12.0.?	$[(12, 32)]$
1827.c1	1827a1	1827.c	1827a	$1$	$1$	\( 3^{2} \cdot 7 \cdot 29 \)	\( - 3^{6} \cdot 7^{2} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$116$	$2$	$0$	$0.787053694$	$1$		$2$	$240$	$-0.166884$	$-1/1421$	$1.01742$	$2.83679$	$[1, -1, 0, 0, 49]$	\(y^2+xy=x^3-x^2+49\)	116.2.0.?	$[(0, 7)]$
1827.d1	1827b3	1827.d	1827b	$6$	$8$	\( 3^{2} \cdot 7 \cdot 29 \)	\( 3^{9} \cdot 7^{2} \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.3	2B	$9744$	$192$	$1$	$14.70845778$	$1$		$0$	$12288$	$1.839968$	$947531277805646290177/38367$	$1.01996$	$7.30878$	$[1, -1, 0, -1841616, -961476971]$	\(y^2+xy=x^3-x^2-1841616x-961476971\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0-8.n.1.5, $\ldots$	$[(4503639/50, 4831881187/50)]$
1827.d2	1827b5	1827.d	1827b	$6$	$8$	\( 3^{2} \cdot 7 \cdot 29 \)	\( 3^{30} \cdot 7 \cdot 29^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.14	2B	$9744$	$192$	$1$	$7.354228891$	$1$		$0$	$24576$	$2.186543$	$8471112631466271697/1662662681263647$	$1.00847$	$6.68069$	$[1, -1, 0, -382221, 74033554]$	\(y^2+xy=x^3-x^2-382221x+74033554\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 16.24.0-8.n.1.6, $\ldots$	$[(8870/7, 1093604/7)]$
1827.d3	1827b4	1827.d	1827b	$6$	$8$	\( 3^{2} \cdot 7 \cdot 29 \)	\( 3^{18} \cdot 7^{2} \cdot 29^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.17	2Cs	$4872$	$192$	$1$	$14.70845778$	$1$		$2$	$12288$	$1.839968$	$244883173420511137/18418027974129$	$1.08831$	$6.20886$	$[1, -1, 0, -117306, -14395073]$	\(y^2+xy=x^3-x^2-117306x-14395073\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 12.24.0-4.b.1.1, 24.48.0-24.i.1.2, $\ldots$	$[(5712231/62, 13073380789/62)]$
1827.d4	1827b2	1827.d	1827b	$6$	$8$	\( 3^{2} \cdot 7 \cdot 29 \)	\( 3^{12} \cdot 7^{4} \cdot 29^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.9	2Cs	$4872$	$192$	$1$	$7.354228891$	$1$		$2$	$6144$	$1.493395$	$231331938231569617/1472026689$	$0.98909$	$6.20128$	$[1, -1, 0, -115101, -15001448]$	\(y^2+xy=x^3-x^2-115101x-15001448\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.3, 12.24.0-4.b.1.3, 24.48.0-24.i.2.2, $\ldots$	$[(5943/2, 438907/2)]$
1827.d5	1827b1	1827.d	1827b	$6$	$8$	\( 3^{2} \cdot 7 \cdot 29 \)	\( - 3^{9} \cdot 7^{8} \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.87	2B	$9744$	$192$	$1$	$3.677114445$	$1$		$3$	$3072$	$1.146820$	$-53297461115137/4513839183$	$0.94722$	$5.10426$	$[1, -1, 0, -7056, -242501]$	\(y^2+xy=x^3-x^2-7056x-242501\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 12.12.0-4.c.1.2, 24.48.0-24.bz.1.7, $\ldots$	$[(1470, 55517)]$
1827.d6	1827b6	1827.d	1827b	$6$	$8$	\( 3^{2} \cdot 7 \cdot 29 \)	\( - 3^{12} \cdot 7 \cdot 29^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.89	2B	$9744$	$192$	$1$	$29.41691556$	$1$		$0$	$24576$	$2.186543$	$215015459663151503/2552757445339983$	$1.02586$	$6.58716$	$[1, -1, 0, 112329, -64042160]$	\(y^2+xy=x^3-x^2+112329x-64042160\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 12.12.0-4.c.1.1, 14.6.0.b.1, $\ldots$	$[(5047493410335/58838, 11369659432888723585/58838)]$
1827.e1	1827e2	1827.e	1827e	$2$	$5$	\( 3^{2} \cdot 7 \cdot 29 \)	\( - 3^{6} \cdot 7 \cdot 29^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$6090$	$48$	$1$	$1$	$1$		$0$	$7200$	$1.134890$	$-1099616058781696/143578043$	$1.03288$	$5.48912$	$[0, 0, 1, -19353, 1036381]$	\(y^2+y=x^3-19353x+1036381\)	5.12.0.a.2, 15.24.0-5.a.2.1, 406.2.0.?, 2030.24.1.?, 6090.48.1.?	$[]$
1827.e2	1827e1	1827.e	1827e	$2$	$5$	\( 3^{2} \cdot 7 \cdot 29 \)	\( - 3^{6} \cdot 7^{5} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$6090$	$48$	$1$	$1$	$1$		$0$	$1440$	$0.330171$	$841232384/487403$	$1.28149$	$3.61391$	$[0, 0, 1, 177, 31]$	\(y^2+y=x^3+177x+31\)	5.12.0.a.1, 15.24.0-5.a.1.1, 406.2.0.?, 2030.24.1.?, 6090.48.1.?	$[]$