Elliptic curves over Q\Q of conductor 11109

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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
11109.a1	11109a1	11109.a	11109a	$1$	$1$	$3 \cdot 7 \cdot 23^{2}$	$- 3^{7} \cdot 7^{3} \cdot 23^{9}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$966$	$2$	$0$	$1$	$1$		$0$	$231840$	$2.166809$	$929714176/750141$	$0.97832$	$5.24607$	$[0, -1, 1, 247396, -29820754]$	$y^2+y=x^3-x^2+247396x-29820754$	966.2.0.?	$[]$
11109.b1	11109b1	11109.b	11109b	$1$	$1$	$3 \cdot 7 \cdot 23^{2}$	$- 3^{7} \cdot 7^{3} \cdot 23^{3}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$966$	$2$	$0$	$0.481012704$	$1$		$6$	$10080$	$0.599062$	$929714176/750141$	$0.97832$	$3.22654$	$[0, -1, 1, 468, 2288]$	$y^2+y=x^3-x^2+468x+2288$	966.2.0.?	$[(8, 80)]$
11109.c1	11109j1	11109.c	11109j	$1$	$1$	$3 \cdot 7 \cdot 23^{2}$	$- 3^{2} \cdot 7^{2} \cdot 23^{8}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.2.0.1		$168$	$4$	$0$	$1$	$1$		$0$	$30912$	$1.356558$	$-8231953/441$	$0.83649$	$4.41157$	$[1, 0, 0, -17997, -972846]$	$y^2+xy=x^3-17997x-972846$	4.2.0.a.1, 168.4.0.?	$[]$
11109.d1	11109i5	11109.d	11109i	$6$	$8$	$3 \cdot 7 \cdot 23^{2}$	$3 \cdot 7^{2} \cdot 23^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$7728$	$192$	$1$	$1$	$1$		$0$	$50688$	$1.641953$	$53297461115137/147$	$1.05087$	$5.41246$	$[1, 0, 0, -414747, 102772518]$	$y^2+xy=x^3-414747x+102772518$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$	$[]$
11109.d2	11109i4	11109.d	11109i	$6$	$8$	$3 \cdot 7 \cdot 23^{2}$	$3^{2} \cdot 7^{4} \cdot 23^{6}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.18	2Cs	$3864$	$192$	$1$	$1$	$1$		$2$	$25344$	$1.295380$	$13027640977/21609$	$1.08149$	$4.51970$	$[1, 0, 0, -25932, 1602855]$	$y^2+xy=x^3-25932x+1602855$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 24.48.0.j.2, $\ldots$	$[]$
11109.d3	11109i3	11109.d	11109i	$6$	$8$	$3 \cdot 7 \cdot 23^{2}$	$3^{8} \cdot 7 \cdot 23^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$7728$	$192$	$1$	$1$	$1$		$0$	$25344$	$1.295380$	$6570725617/45927$	$1.00160$	$4.44622$	$[1, 0, 0, -20642, -1136307]$	$y^2+xy=x^3-20642x-1136307$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 48.48.0.bf.1, $\ldots$	$[]$
11109.d4	11109i6	11109.d	11109i	$6$	$8$	$3 \cdot 7 \cdot 23^{2}$	$- 3 \cdot 7^{8} \cdot 23^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$7728$	$192$	$1$	$1$	$1$		$0$	$50688$	$1.641953$	$-4354703137/17294403$	$1.04266$	$4.62343$	$[1, 0, 0, -17997, 2604252]$	$y^2+xy=x^3-17997x+2604252$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$	$[]$
11109.d5	11109i2	11109.d	11109i	$6$	$8$	$3 \cdot 7 \cdot 23^{2}$	$3^{4} \cdot 7^{2} \cdot 23^{6}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.10	2Cs	$3864$	$192$	$1$	$1$	$1$		$2$	$12672$	$0.948805$	$7189057/3969$	$1.14862$	$3.71435$	$[1, 0, 0, -2127, 7920]$	$y^2+xy=x^3-2127x+7920$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$	$[]$
11109.d6	11109i1	11109.d	11109i	$6$	$8$	$3 \cdot 7 \cdot 23^{2}$	$- 3^{2} \cdot 7 \cdot 23^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.1	2B	$7728$	$192$	$1$	$1$	$1$		$1$	$6336$	$0.602232$	$103823/63$	$0.97868$	$3.25945$	$[1, 0, 0, 518, 1043]$	$y^2+xy=x^3+518x+1043$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$	$[]$
11109.e1	11109e1	11109.e	11109e	$1$	$1$	$3 \cdot 7 \cdot 23^{2}$	$- 3^{2} \cdot 7^{2} \cdot 23^{2}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.2.0.1		$3864$	$4$	$0$	$0.341374732$	$1$		$6$	$1344$	$-0.211189$	$-8231953/441$	$0.83649$	$2.39204$	$[1, 0, 0, -34, 77]$	$y^2+xy=x^3-34x+77$	4.2.0.a.1, 3864.4.0.?	$[(-1, 11)]$
11109.f1	11109d1	11109.f	11109d	$1$	$1$	$3 \cdot 7 \cdot 23^{2}$	$3 \cdot 7^{3} \cdot 23^{8}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$42$	$2$	$0$	$2.606124536$	$1$		$0$	$39744$	$1.504950$	$160261033/1029$	$0.87602$	$4.72076$	$[1, 0, 1, -48415, 4073417]$	$y^2+xy+y=x^3-48415x+4073417$	42.2.0.a.1	$[(925/3, 10237/3)]$
11109.g1	11109c2	11109.g	11109c	$2$	$2$	$3 \cdot 7 \cdot 23^{2}$	$3^{4} \cdot 7^{8} \cdot 23^{3}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.128	2B	$7728$	$192$	$9$	$3.139374207$	$1$		$0$	$16896$	$1.192419$	$6163717745375/466948881$	$0.98902$	$4.17113$	$[1, 0, 1, -8786, -296215]$	$y^2+xy+y=x^3-8786x-296215$	2.3.0.a.1, 4.6.0.e.1, 8.24.0.bi.1, 48.48.1.fo.1, 92.12.0.?, $\ldots$	$[(-261/2, 395/2)]$
11109.g2	11109c1	11109.g	11109c	$2$	$2$	$3 \cdot 7 \cdot 23^{2}$	$- 3^{8} \cdot 7^{4} \cdot 23^{3}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.83	2B	$7728$	$192$	$9$	$1.569687103$	$1$		$5$	$8448$	$0.845845$	$1349232625/15752961$	$0.98873$	$3.58358$	$[1, 0, 1, 529, -20491]$	$y^2+xy+y=x^3+529x-20491$	2.3.0.a.1, 4.12.0.f.1, 8.24.0.bt.1, 46.6.0.a.1, 48.48.1.fv.1, $\ldots$	$[(69, 553)]$
11109.h1	11109g2	11109.h	11109g	$2$	$2$	$3 \cdot 7 \cdot 23^{2}$	$3^{4} \cdot 7^{8} \cdot 23^{9}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.128	2B	$7728$	$192$	$9$	$1$	$1$		$0$	$388608$	$2.760166$	$6163717745375/466948881$	$0.98902$	$6.19066$	$[1, 0, 1, -4647541, 3594749789]$	$y^2+xy+y=x^3-4647541x+3594749789$	2.3.0.a.1, 4.6.0.e.1, 8.24.0.bi.1, 48.48.1.fo.1, 92.12.0.?, $\ldots$	$[]$
11109.h2	11109g1	11109.h	11109g	$2$	$2$	$3 \cdot 7 \cdot 23^{2}$	$- 3^{8} \cdot 7^{4} \cdot 23^{9}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.83	2B	$7728$	$192$	$9$	$1$	$1$		$1$	$194304$	$2.413593$	$1349232625/15752961$	$0.98873$	$5.60311$	$[1, 0, 1, 280094, 249871151]$	$y^2+xy+y=x^3+280094x+249871151$	2.3.0.a.1, 4.12.0.f.1, 8.24.0.bt.1, 46.6.0.a.1, 48.48.1.fv.1, $\ldots$	$[]$
11109.i1	11109h1	11109.i	11109h	$1$	$1$	$3 \cdot 7 \cdot 23^{2}$	$3 \cdot 7^{3} \cdot 23^{2}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$42$	$2$	$0$	$1$	$1$		$0$	$1728$	$-0.062798$	$160261033/1029$	$0.87602$	$2.70123$	$[1, 0, 1, -92, -343]$	$y^2+xy+y=x^3-92x-343$	42.2.0.a.1	$[]$
11109.j1	11109k1	11109.j	11109k	$1$	$1$	$3 \cdot 7 \cdot 23^{2}$	$- 3^{5} \cdot 7 \cdot 23^{9}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$966$	$2$	$0$	$1$	$1$		$0$	$158400$	$1.693268$	$-98867482624/20696067$	$1.05025$	$4.77041$	$[0, 1, 1, -50960, 5150045]$	$y^2+y=x^3+x^2-50960x+5150045$	966.2.0.?	$[]$
11109.k1	11109f1	11109.k	11109f	$1$	$1$	$3 \cdot 7 \cdot 23^{2}$	$- 3 \cdot 7 \cdot 23^{7}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$966$	$2$	$0$	$4.238567559$	$1$		$0$	$10560$	$0.769917$	$512000/483$	$0.74348$	$3.43073$	$[0, 1, 1, 882, -7705]$	$y^2+y=x^3+x^2+882x-7705$	966.2.0.?	$[(2225/8, 131465/8)]$

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