Elliptic curves over $\Q$ of conductor 2166

Results (18 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
2166.a1	2166b3	2166.a	2166b	$4$	$6$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{2} \cdot 3 \cdot 19^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.4, 3.4.0.1	2B, 3B	$456$	$96$	$1$	$1$	$1$		$1$	$12960$	$1.577721$	$8671983378625/82308$	$1.00775$	$6.17888$	$[1, 1, 0, -154515, 23313369]$	\(y^2+xy=x^3+x^2-154515x+23313369\)	2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.1, 8.6.0.d.1, 24.48.0-24.bx.1.2, $\ldots$	$[]$
2166.a2	2166b4	2166.a	2166b	$4$	$6$	\( 2 \cdot 3 \cdot 19^{2} \)	\( - 2 \cdot 3^{2} \cdot 19^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.5, 3.4.0.1	2B, 3B	$456$	$96$	$1$	$1$	$1$		$0$	$25920$	$1.924295$	$-8078253774625/846825858$	$1.01015$	$6.19132$	$[1, 1, 0, -150905, 24459183]$	\(y^2+xy=x^3+x^2-150905x+24459183\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.a.1, 12.24.0-6.a.1.11, $\ldots$	$[]$
2166.a3	2166b1	2166.a	2166b	$4$	$6$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{6} \cdot 3^{3} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.4, 3.4.0.1	2B, 3B	$456$	$96$	$1$	$1$	$1$		$1$	$4320$	$1.028416$	$57066625/32832$	$1.04766$	$4.62544$	$[1, 1, 0, -2895, -5787]$	\(y^2+xy=x^3+x^2-2895x-5787\)	2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.3, 8.6.0.d.1, 24.48.0-24.bx.1.6, $\ldots$	$[]$
2166.a4	2166b2	2166.a	2166b	$4$	$6$	\( 2 \cdot 3 \cdot 19^{2} \)	\( - 2^{3} \cdot 3^{6} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.5, 3.4.0.1	2B, 3B	$456$	$96$	$1$	$1$	$1$		$0$	$8640$	$1.374989$	$3616805375/2105352$	$1.07346$	$5.16565$	$[1, 1, 0, 11545, -31779]$	\(y^2+xy=x^3+x^2+11545x-31779\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.a.1, 12.24.0-6.a.1.5, $\ldots$	$[]$
2166.b1	2166a1	2166.b	2166a	$1$	$1$	\( 2 \cdot 3 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{5} \cdot 19^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.258394025$	$1$		$6$	$1440$	$0.658456$	$-1100553625/62208$	$1.03685$	$4.25616$	$[1, 1, 0, -1090, 14068]$	\(y^2+xy=x^3+x^2-1090x+14068\)	6.2.0.a.1	$[(36, 134)]$
2166.c1	2166e1	2166.c	2166e	$1$	$1$	\( 2 \cdot 3 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{9} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.092009828$	$1$		$12$	$1296$	$0.231059$	$205083359/314928$	$1.00799$	$3.32404$	$[1, 0, 1, 87, 412]$	\(y^2+xy+y=x^3+87x+412\)	6.2.0.a.1	$[(-1, 18)]$
2166.d1	2166d3	2166.d	2166d	$4$	$4$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{5} \cdot 3^{3} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$5.305871388$	$1$		$0$	$86400$	$2.573658$	$74220219816682217473/16416$	$1.10905$	$8.25715$	$[1, 0, 1, -31606280, 68389818806]$	\(y^2+xy+y=x^3-31606280x+68389818806\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.1, 24.24.0-8.m.1.3, $\ldots$	$[(81156/5, -196894/5)]$
2166.d2	2166d2	2166.d	2166d	$4$	$4$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{6} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.4	2Cs	$456$	$48$	$0$	$2.652935694$	$1$		$6$	$43200$	$2.227085$	$18120364883707393/269485056$	$1.09068$	$7.17420$	$[1, 0, 1, -1975400, 1068459446]$	\(y^2+xy+y=x^3-1975400x+1068459446\)	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.3, 76.12.0.?, $\ldots$	$[(777, 1291)]$
2166.d3	2166d4	2166.d	2166d	$4$	$4$	\( 2 \cdot 3 \cdot 19^{2} \)	\( - 2^{5} \cdot 3^{12} \cdot 19^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.16	2B	$456$	$48$	$0$	$1.326467847$	$1$		$6$	$86400$	$2.573658$	$-16576888679672833/2216253521952$	$1.04427$	$7.18967$	$[1, 0, 1, -1917640, 1133889974]$	\(y^2+xy+y=x^3-1917640x+1133889974\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 24.24.0-8.d.1.3, 76.12.0.?, $\ldots$	$[(-464, 44093)]$
2166.d4	2166d1	2166.d	2166d	$4$	$4$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{20} \cdot 3^{3} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$1.326467847$	$1$		$3$	$21600$	$1.880512$	$4824238966273/537919488$	$1.00823$	$6.10253$	$[1, 0, 1, -127080, 15656374]$	\(y^2+xy+y=x^3-127080x+15656374\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.1, $\ldots$	$[(68, 2673)]$
2166.e1	2166c2	2166.e	2166c	$2$	$2$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{14} \cdot 19^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$0$	$85120$	$2.425694$	$248028267187/76527504$	$1.06020$	$6.86620$	$[1, 0, 1, -897815, -223797814]$	\(y^2+xy+y=x^3-897815x-223797814\)	2.3.0.a.1, 12.6.0.g.1, 76.6.0.?, 228.12.0.?	$[]$
2166.e2	2166c1	2166.e	2166c	$2$	$2$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{7} \cdot 19^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$42560$	$2.079121$	$14580432307/559872$	$1.02951$	$6.49723$	$[1, 0, 1, -349095, 76681258]$	\(y^2+xy+y=x^3-349095x+76681258\)	2.3.0.a.1, 12.6.0.g.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[]$
2166.f1	2166g1	2166.f	2166g	$1$	$1$	\( 2 \cdot 3 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{9} \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$24624$	$1.703279$	$205083359/314928$	$1.00799$	$5.62419$	$[1, 1, 1, 31580, -2764459]$	\(y^2+xy+y=x^3+x^2+31580x-2764459\)	6.2.0.a.1	$[]$
2166.g1	2166f2	2166.g	2166f	$2$	$2$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{14} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$0$	$4480$	$0.953473$	$248028267187/76527504$	$1.06020$	$4.56604$	$[1, 1, 1, -2487, 31581]$	\(y^2+xy+y=x^3+x^2-2487x+31581\)	2.3.0.a.1, 12.6.0.g.1, 76.6.0.?, 228.12.0.?	$[]$
2166.g2	2166f1	2166.g	2166f	$2$	$2$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{7} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$2240$	$0.606900$	$14580432307/559872$	$1.02951$	$4.19708$	$[1, 1, 1, -967, -11587]$	\(y^2+xy+y=x^3+x^2-967x-11587\)	2.3.0.a.1, 12.6.0.g.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[]$
2166.h1	2166h1	2166.h	2166h	$1$	$1$	\( 2 \cdot 3 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{5} \cdot 19^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$27360$	$2.130676$	$-1100553625/62208$	$1.03685$	$6.55631$	$[1, 0, 0, -393678, -99641340]$	\(y^2+xy=x^3-393678x-99641340\)	6.2.0.a.1	$[]$
2166.i1	2166i1	2166.i	2166i	$2$	$2$	\( 2 \cdot 3 \cdot 19^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$456$	$12$	$0$	$1$	$1$		$1$	$7200$	$1.291529$	$96386901625/18468$	$0.97983$	$5.59306$	$[1, 0, 0, -34483, 2461373]$	\(y^2+xy=x^3-34483x+2461373\)	2.3.0.a.1, 8.6.0.d.1, 114.6.0.?, 456.12.0.?	$[]$
2166.i2	2166i2	2166.i	2166i	$2$	$2$	\( 2 \cdot 3 \cdot 19^{2} \)	\( - 2 \cdot 3^{10} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$456$	$12$	$0$	$1$	$1$		$0$	$14400$	$1.638102$	$-69173457625/42633378$	$0.99175$	$5.64428$	$[1, 0, 0, -30873, 2997819]$	\(y^2+xy=x^3-30873x+2997819\)	2.3.0.a.1, 8.6.0.a.1, 228.6.0.?, 456.12.0.?	$[]$