LMFDB - Elliptic curves over $\Q$ of conductor 1089

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (23 matches)

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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	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1089.a1	1089k1	1089.a	1089k	$1$	$1$	$ 3^{2} \cdot 11^{2} $	$ - 3^{9} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$					$6$	$2$	$0$	$0.177816633$	$1$	$8$	$288$	$-0.087104$	$45056/27$	$1.13667$	$3.16074$	$[0, 0, 1, 33, -14]$	$y^2+y=x^3+33x-14$	6.2.0.a.1	$[(4, 13)]$
1089.b1	1089j3	1089.b	1089j	$3$	$25$	$ 3^{2} \cdot 11^{2} $	$ - 3^{6} \cdot 11^{7} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	25.60.0.2	5B.4.2	$1650$	$1200$	$37$	$7.655751664$	$1$	$0$	$18000$	$2.244965$	$-52893159101157376/11$	$1.09296$	$8.50650$	$[0, 0, 1, -8516343, -9565943918]$	$y^2+y=x^3-8516343x-9565943918$	5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 30.24.0-5.a.2.1, 110.24.1.?, $\ldots$	$[(35585/2, 6292843/2)]$
1089.b2	1089j2	1089.b	1089j	$3$	$25$	$ 3^{2} \cdot 11^{2} $	$ - 3^{6} \cdot 11^{11} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	5.60.0.1	5Cs.4.1	$1650$	$1200$	$37$	$1.531150332$	$1$	$0$	$3600$	$1.440245$	$-122023936/161051$	$1.01300$	$5.83251$	$[0, 0, 1, -11253, -832208]$	$y^2+y=x^3-11253x-832208$	5.60.0.a.1, 22.2.0.a.1, 30.120.0-5.a.1.1, 110.120.5.?, 165.120.0.?, $\ldots$	$[(737/2, 14637/2)]$
1089.b3	1089j1	1089.b	1089j	$3$	$25$	$ 3^{2} \cdot 11^{2} $	$ - 3^{6} \cdot 11^{7} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	25.60.0.1	5B.4.1	$1650$	$1200$	$37$	$0.306230066$	$1$	$6$	$720$	$0.635525$	$-4096/11$	$0.82546$	$4.43683$	$[0, 0, 1, -363, 6322]$	$y^2+y=x^3-363x+6322$	5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 30.24.0-5.a.1.1, 110.24.1.?, $\ldots$	$[(11, 60)]$
1089.c1	1089h2	1089.c	1089h	$2$	$11$	$ 3^{2} \cdot 11^{2} $	$ - 3^{6} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2, 11$	4.2.0.1, 11.60.1.3	11B.10.5	$264$	$480$	$16$	$1.460386125$	$1$	$4$	$1584$	$1.230293$	$-24729001$	$0.96853$	$6.12016$	$[1, -1, 1, -32693, -2267130]$	$y^2+xy+y=x^3-x^2-32693x-2267130$	4.2.0.a.1, 11.60.1.b.2, 24.4.0-4.a.1.1, 33.120.1-11.b.2.2, 44.120.6.b.2, $\ldots$	$[(212, 438)]$
1089.c2	1089h1	1089.c	1089h	$2$	$11$	$ 3^{2} \cdot 11^{2} $	$ - 3^{6} \cdot 11^{4} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2, 11$	4.2.0.1, 11.60.1.4	11B.10.4	$264$	$480$	$16$	$0.132762375$	$1$	$6$	$144$	$0.031345$	$-121$	$0.94611$	$3.38990$	$[1, -1, 1, -23, 168]$	$y^2+xy+y=x^3-x^2-23x+168$	4.2.0.a.1, 11.60.1.b.1, 24.4.0-4.a.1.1, 33.120.1-11.b.1.2, 44.120.6.b.1, $\ldots$	$[(14, 42)]$
1089.d1	1089d2	1089.d	1089d	$2$	$2$	$ 3^{2} \cdot 11^{2} $	$ 3^{9} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$	$0$	$2880$	$1.259563$	$19034163/121$	$0.94120$	$5.86823$	$[1, -1, 1, -18173, 942274]$	$y^2+xy+y=x^3-x^2-18173x+942274$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.?	$[]$
1089.d2	1089d1	1089.d	1089d	$2$	$2$	$ 3^{2} \cdot 11^{2} $	$ 3^{9} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$	$1$	$1440$	$0.912990$	$19683/11$	$1.13667$	$4.88522$	$[1, -1, 1, -1838, -5156]$	$y^2+xy+y=x^3-x^2-1838x-5156$	2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.?	$[]$
1089.e1	1089b1	1089.e	1089b	$2$	$3$	$ 3^{2} \cdot 11^{2} $	$ - 3^{3} \cdot 11^{10} $	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$	✓	$11$	11.165.5.1	11Nn.1.4				$1$	$1$	$0$	$1232$	$0.951781$	$0$		$4.96631$	$[0, 0, 1, 0, -40263]$	$y^2+y=x^3-40263$		$[]$
1089.e2	1089b2	1089.e	1089b	$2$	$3$	$ 3^{2} \cdot 11^{2} $	$ - 3^{9} \cdot 11^{10} $	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$	✓	$11$	11.165.5.1	11Nn.1.4				$1$	$1$	$0$	$3696$	$1.501087$	$0$		$5.90892$	$[0, 0, 1, 0, 1087094]$	$y^2+y=x^3+1087094$		$[]$
1089.f1	1089a2	1089.f	1089a	$2$	$3$	$ 3^{2} \cdot 11^{2} $	$ - 3^{9} \cdot 11^{4} $	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$	✓	$3, 11$	27.648.18.4, 11.165.5.1	3B.1.2, 11Nn.1.4				$1$	$1$	$0$	$336$	$0.302140$	$0$		$3.85153$	$[0, 0, 1, 0, -817]$	$y^2+y=x^3-817$		$[]$
1089.f2	1089a1	1089.f	1089a	$2$	$3$	$ 3^{2} \cdot 11^{2} $	$ - 3^{3} \cdot 11^{4} $	$0$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$	✓	$3, 11$	27.648.18.1, 11.165.5.1	3B.1.1, 11Nn.1.4				$1$	$1$	$2$	$112$	$-0.247166$	$0$		$2.90892$	$[0, 0, 1, 0, 30]$	$y^2+y=x^3+30$		$[]$
1089.g1	1089e2	1089.g	1089e	$2$	$11$	$ 3^{2} \cdot 11^{2} $	$ - 3^{6} \cdot 11^{9} $	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-11})$	$-11$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$0$	$1320$	$1.125181$	$-32768$	$1.02512$	$5.52284$	$[0, 0, 1, -7986, 281839]$	$y^2+y=x^3-7986x+281839$		$[]$
1089.g2	1089e1	1089.g	1089e	$2$	$11$	$ 3^{2} \cdot 11^{2} $	$ - 3^{6} \cdot 11^{3} $	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-11})$	$-11$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$0$	$120$	$-0.073767$	$-32768$	$1.02512$	$3.46545$	$[0, 0, 1, -66, -212]$	$y^2+y=x^3-66x-212$		$[]$
1089.h1	1089c2	1089.h	1089c	$2$	$2$	$ 3^{2} \cdot 11^{2} $	$ 3^{3} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$	$0$	$960$	$0.710258$	$19034163/121$	$0.94120$	$4.92562$	$[1, -1, 0, -2019, -34226]$	$y^2+xy=x^3-x^2-2019x-34226$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.?	$[]$
1089.h2	1089c1	1089.h	1089c	$2$	$2$	$ 3^{2} \cdot 11^{2} $	$ 3^{3} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$	$1$	$480$	$0.363684$	$19683/11$	$1.13667$	$3.94261$	$[1, -1, 0, -204, 259]$	$y^2+xy=x^3-x^2-204x+259$	2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.?	$[]$
1089.i1	1089f2	1089.i	1089f	$2$	$11$	$ 3^{2} \cdot 11^{2} $	$ - 3^{6} \cdot 11^{10} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2, 11$	4.2.0.1, 11.60.1.4	11B.10.4	$264$	$480$	$16$	$5.138097620$	$1$	$2$	$1584$	$1.230293$	$-121$	$0.94611$	$5.44730$	$[1, -1, 0, -2745, -215726]$	$y^2+xy=x^3-x^2-2745x-215726$	4.2.0.a.1, 11.60.1.b.1, 33.120.1-11.b.1.1, 44.120.6.b.1, 88.240.16.?, $\ldots$	$[(470, 9872)]$
1089.i2	1089f1	1089.i	1089f	$2$	$11$	$ 3^{2} \cdot 11^{2} $	$ - 3^{6} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2, 11$	4.2.0.1, 11.60.1.3	11B.10.5	$264$	$480$	$16$	$0.467099783$	$1$	$2$	$144$	$0.031345$	$-24729001$	$0.96853$	$4.06277$	$[1, -1, 0, -270, 1777]$	$y^2+xy=x^3-x^2-270x+1777$	4.2.0.a.1, 11.60.1.b.2, 33.120.1-11.b.2.1, 44.120.6.b.2, 88.240.16.?, $\ldots$	$[(8, 5)]$
1089.j1	1089g3	1089.j	1089g	$4$	$4$	$ 3^{2} \cdot 11^{2} $	$ 3^{9} \cdot 11^{10} $	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.12.0.14	2B	$264$	$48$	$0$	$2.957701004$	$1$	$2$	$5760$	$1.735622$	$347873904937/395307$	$1.00913$	$6.80024$	$[1, -1, 0, -159561, 24548134]$	$y^2+xy=x^3-x^2-159561x+24548134$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 12.12.0.h.1, 24.24.0-12.h.1.4, $\ldots$	$[(-382, 5636)]$
1089.j2	1089g2	1089.j	1089g	$4$	$4$	$ 3^{2} \cdot 11^{2} $	$ 3^{12} \cdot 11^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	4.12.0.2	2Cs	$132$	$48$	$0$	$5.915402008$	$1$	$2$	$2880$	$1.389048$	$169112377/88209$	$1.00669$	$5.70929$	$[1, -1, 0, -12546, 173047]$	$y^2+xy=x^3-x^2-12546x+173047$	2.6.0.a.1, 4.12.0-2.a.1.2, 12.24.0-12.a.1.4, 44.24.0-44.b.1.4, 132.48.0.?	$[(5603/2, 412357/2)]$
1089.j3	1089g1	1089.j	1089g	$4$	$4$	$ 3^{2} \cdot 11^{2} $	$ 3^{9} \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.12.0.14	2B	$264$	$48$	$0$	$2.957701004$	$1$	$3$	$1440$	$1.042475$	$30664297/297$	$1.09706$	$5.46512$	$[1, -1, 0, -7101, -226616]$	$y^2+xy=x^3-x^2-7101x-226616$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.13, $\ldots$	$[(1400, 51572)]$
1089.j4	1089g4	1089.j	1089g	$4$	$4$	$ 3^{2} \cdot 11^{2} $	$ - 3^{18} \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.12.0.14	2B	$264$	$48$	$0$	$2.957701004$	$1$	$0$	$5760$	$1.735622$	$9090072503/5845851$	$1.03763$	$6.27905$	$[1, -1, 0, 47349, 1311052]$	$y^2+xy=x^3-x^2+47349x+1311052$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 12.12.0-4.c.1.1, 22.6.0.a.1, $\ldots$	$[(419/2, 21361/2)]$
1089.k1	1089i1	1089.k	1089i	$1$	$1$	$ 3^{2} \cdot 11^{2} $	$ - 3^{9} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$					$6$	$2$	$0$	$0.677917086$	$1$	$0$	$3168$	$1.111843$	$45056/27$	$1.13667$	$5.21814$	$[0, 0, 1, 3993, 18301]$	$y^2+y=x^3+3993x+18301$	6.2.0.a.1	$[(121/2, 3263/2)]$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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