Elliptic curves over $\Q$ of conductor 1287

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
1287.a1	1287a2	1287.a	1287a	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13 \)	\( 3^{3} \cdot 11^{2} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1.267437983$	$1$		$6$	$960$	$0.740729$	$23835655373139/584043889$	$0.96323$	$4.76225$	$[1, -1, 1, -1799, -28284]$	\(y^2+xy+y=x^3-x^2-1799x-28284\)	2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.?	$[(-22, 27)]$
1287.a2	1287a1	1287.a	1287a	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13 \)	\( - 3^{3} \cdot 11^{4} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$2.534875966$	$1$		$5$	$480$	$0.394156$	$17779581/32166277$	$1.02883$	$3.91570$	$[1, -1, 1, 16, -1422]$	\(y^2+xy+y=x^3-x^2+16x-1422\)	2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.?	$[(14, 30)]$
1287.b1	1287d1	1287.b	1287d	$1$	$1$	\( 3^{2} \cdot 11 \cdot 13 \)	\( - 3^{6} \cdot 11 \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$0.500673664$	$1$		$4$	$120$	$-0.140192$	$-262144/1859$	$0.89320$	$3.02408$	$[0, 0, 1, -12, 58]$	\(y^2+y=x^3-12x+58\)	22.2.0.a.1	$[(2, 6)]$
1287.c1	1287b2	1287.c	1287b	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13 \)	\( 3^{9} \cdot 11^{2} \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$0$	$2880$	$1.290035$	$23835655373139/584043889$	$0.96323$	$5.68287$	$[1, -1, 0, -16188, 779849]$	\(y^2+xy=x^3-x^2-16188x+779849\)	2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.?	$[]$
1287.c2	1287b1	1287.c	1287b	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13 \)	\( - 3^{9} \cdot 11^{4} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$1440$	$0.943462$	$17779581/32166277$	$1.02883$	$4.83631$	$[1, -1, 0, 147, 38240]$	\(y^2+xy=x^3-x^2+147x+38240\)	2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.?	$[]$
1287.d1	1287c2	1287.d	1287c	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13 \)	\( 3^{7} \cdot 11^{2} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1716$	$12$	$0$	$1.074532553$	$1$		$4$	$256$	$0.177942$	$244140625/61347$	$1.08894$	$3.61797$	$[1, -1, 0, -117, -338]$	\(y^2+xy=x^3-x^2-117x-338\)	2.3.0.a.1, 12.6.0.a.1, 572.6.0.?, 1716.12.0.?	$[(-6, 14)]$
1287.d2	1287c1	1287.d	1287c	$2$	$2$	\( 3^{2} \cdot 11 \cdot 13 \)	\( - 3^{8} \cdot 11 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1716$	$12$	$0$	$2.149065107$	$1$		$3$	$128$	$-0.168632$	$857375/1287$	$0.79548$	$2.89375$	$[1, -1, 0, 18, -41]$	\(y^2+xy=x^3-x^2+18x-41\)	2.3.0.a.1, 12.6.0.b.1, 286.6.0.?, 1716.12.0.?	$[(6, 13)]$
1287.e1	1287e3	1287.e	1287e	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13 \)	\( 3^{8} \cdot 11 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$6864$	$192$	$1$	$1$	$16$	$2$	$0$	$2048$	$1.090403$	$35765103905346817/1287$	$0.98956$	$6.24399$	$[1, -1, 0, -61776, -5894451]$	\(y^2+xy=x^3-x^2-61776x-5894451\)	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.1.8, $\ldots$	$[]$
1287.e2	1287e5	1287.e	1287e	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13 \)	\( 3^{7} \cdot 11^{8} \cdot 13^{2} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.46	2B	$6864$	$192$	$1$	$1$	$1$		$2$	$4096$	$1.436975$	$3013001140430737/108679952667$	$0.97853$	$5.89846$	$[1, -1, 0, -27081, 1667790]$	\(y^2+xy=x^3-x^2-27081x+1667790\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 12.24.0-12.h.1.2, 24.48.0-24.bl.1.9, $\ldots$	$[]$
1287.e3	1287e4	1287.e	1287e	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13 \)	\( 3^{8} \cdot 11^{4} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.3	2Cs	$3432$	$192$	$1$	$1$	$1$		$2$	$2048$	$1.090403$	$11779205551777/3763454409$	$0.95747$	$5.12412$	$[1, -1, 0, -4266, -70713]$	\(y^2+xy=x^3-x^2-4266x-70713\)	2.6.0.a.1, 4.24.0-4.b.1.2, 12.48.0-12.c.1.2, 88.48.0.?, 104.48.0.?, $\ldots$	$[]$
1287.e4	1287e2	1287.e	1287e	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13 \)	\( 3^{10} \cdot 11^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.24	2Cs	$3432$	$192$	$1$	$1$	$4$	$2$	$2$	$1024$	$0.743828$	$8732907467857/1656369$	$0.94339$	$5.08232$	$[1, -1, 0, -3861, -91368]$	\(y^2+xy=x^3-x^2-3861x-91368\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.5, 12.24.0-4.b.1.3, 24.48.0-24.m.1.1, $\ldots$	$[]$
1287.e5	1287e1	1287.e	1287e	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13 \)	\( - 3^{14} \cdot 11 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$6864$	$192$	$1$	$1$	$4$	$2$	$1$	$512$	$0.397254$	$-1532808577/938223$	$0.88405$	$3.97533$	$[1, -1, 0, -216, -1701]$	\(y^2+xy=x^3-x^2-216x-1701\)	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.1.8, $\ldots$	$[]$
1287.e6	1287e6	1287.e	1287e	$6$	$8$	\( 3^{2} \cdot 11 \cdot 13 \)	\( - 3^{7} \cdot 11^{2} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.56	2B	$6864$	$192$	$1$	$1$	$1$		$0$	$4096$	$1.436975$	$266679605718863/296110251723$	$0.98475$	$5.55983$	$[1, -1, 0, 12069, -492156]$	\(y^2+xy=x^3-x^2+12069x-492156\)	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 8.24.0-8.n.1.10, 12.24.0-12.g.1.1, $\ldots$	$[]$