Elliptic curves over $\Q$ of conductor 1936

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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	Manin constant
1936.a1	1936l2	1936.a	1936l	$2$	$11$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 11$	4.2.0.1, 11.60.1.4	11B.10.4	$88$	$480$	$16$	$4.374833372$	$1$		$2$	$4224$	$1.374134$	$-121$	$0.94611$	$5.26125$	$[0, 1, 0, -4880, -514604]$	\(y^2=x^3+x^2-4880x-514604\)	4.2.0.a.1, 11.60.1.b.1, 22.120.1-11.b.1.2, 44.240.6-44.b.1.4, 88.480.16.?	$[(100, 86)]$	$1$
1936.a2	1936l1	1936.a	1936l	$2$	$11$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 11$	4.2.0.1, 11.60.1.3	11B.10.5	$88$	$480$	$16$	$0.397712124$	$1$		$6$	$384$	$0.175186$	$-24729001$	$0.96853$	$3.98198$	$[0, 1, 0, -480, 3892]$	\(y^2=x^3+x^2-480x+3892\)	4.2.0.a.1, 11.60.1.b.2, 22.120.1-11.b.2.2, 44.240.6-44.b.2.4, 88.480.16.?	$[(12, 2)]$	$1$
1936.b1	1936k2	1936.b	1936k	$2$	$11$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 11$	8.4.0.2, 11.60.1.3	11B.10.5	$88$	$480$	$16$	$2.607222391$	$1$		$2$	$4224$	$1.374134$	$-24729001$	$0.96853$	$5.88296$	$[0, 1, 0, -58120, -5412684]$	\(y^2=x^3+x^2-58120x-5412684\)	4.2.0.a.1, 8.4.0-4.a.1.1, 11.60.1.b.2, 22.120.1-11.b.2.1, 44.240.6-44.b.2.2, $\ldots$	$[(524, 10406)]$	$1$
1936.b2	1936k1	1936.b	1936k	$2$	$11$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 11$	8.4.0.2, 11.60.1.4	11B.10.4	$88$	$480$	$16$	$0.237020217$	$1$		$6$	$384$	$0.175186$	$-121$	$0.94611$	$3.36026$	$[0, 1, 0, -40, 372]$	\(y^2=x^3+x^2-40x+372\)	4.2.0.a.1, 8.4.0-4.a.1.1, 11.60.1.b.1, 22.120.1-11.b.1.1, 44.240.6-44.b.1.2, $\ldots$	$[(-4, 22)]$	$1$
1936.c1	1936h2	1936.c	1936h	$2$	$3$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{8} \cdot 11^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$132$	$16$	$0$	$2.323199861$	$1$		$2$	$2880$	$1.095961$	$-199794688/1331$	$0.99506$	$5.16052$	$[0, -1, 0, -9357, -347279]$	\(y^2=x^3-x^2-9357x-347279\)	3.4.0.a.1, 12.8.0-3.a.1.4, 22.2.0.a.1, 66.8.0.a.1, 132.16.0.?	$[(169, 1694)]$	$1$
1936.c2	1936h1	1936.c	1936h	$2$	$3$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{8} \cdot 11^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$132$	$16$	$0$	$0.774399953$	$1$		$4$	$960$	$0.546654$	$8192/11$	$0.84294$	$3.86098$	$[0, -1, 0, 323, -2671]$	\(y^2=x^3-x^2+323x-2671\)	3.4.0.a.1, 12.8.0-3.a.1.3, 22.2.0.a.1, 66.8.0.a.1, 132.16.0.?	$[(37, 242)]$	$1$
1936.d1	1936b1	1936.d	1936b	$1$	$1$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{8} \cdot 11^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.4.0.1		$44$	$8$	$0$	$2.471616732$	$1$		$0$	$2112$	$0.947543$	$1024$	$0.78666$	$4.50000$	$[0, -1, 0, 1775, -24451]$	\(y^2=x^3-x^2+1775x-24451\)	4.4.0.a.1, 22.2.0.a.1, 44.8.0.a.1	$[(124/3, 1331/3)]$	$1$
1936.e1	1936a1	1936.e	1936a	$1$	$1$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{8} \cdot 11^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.4.0.1		$44$	$8$	$0$	$0.711549097$	$1$		$2$	$192$	$-0.251404$	$1024$	$0.78666$	$2.59902$	$[0, -1, 0, 15, 13]$	\(y^2=x^3-x^2+15x+13\)	4.4.0.a.1, 22.2.0.a.1, 44.8.0.a.1	$[(4, 11)]$	$1$
1936.f1	1936d1	1936.f	1936d	$1$	$1$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{10} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.16.0.2		$4$	$16$	$0$	$1$	$1$		$0$	$2112$	$0.873946$	$-1188$	$0.78666$	$4.50461$	$[0, 0, 0, -1331, 29282]$	\(y^2=x^3-1331x+29282\)	4.16.0-4.b.1.1	$[ ]$	$1$
1936.g1	1936c1	1936.g	1936c	$1$	$1$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{10} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.8.0.2		$44$	$16$	$0$	$1$	$1$		$0$	$192$	$-0.325001$	$-1188$	$0.78666$	$2.60363$	$[0, 0, 0, -11, -22]$	\(y^2=x^3-11x-22\)	4.8.0.b.1, 44.16.0-4.b.1.1	$[ ]$	$1$
1936.h1	1936f2	1936.h	1936f	$2$	$11$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{9} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-11})$	$-11$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$0$	$3168$	$1.269022$	$-32768$	$1.02512$	$5.33105$	$[0, 1, 0, -14197, 663331]$	\(y^2=x^3+x^2-14197x+663331\)		$[ ]$	$1$
1936.h2	1936f1	1936.h	1936f	$2$	$11$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{3} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-11})$	$-11$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$0$	$288$	$0.070074$	$-32768$	$1.02512$	$3.43007$	$[0, 1, 0, -117, -541]$	\(y^2=x^3+x^2-117x-541\)		$[ ]$	$1$
1936.i1	1936g3	1936.i	1936g	$3$	$25$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.2	5B.4.2	$1100$	$1200$	$37$	$22.07430201$	$1$		$0$	$24000$	$2.388805$	$-52893159101157376/11$	$1.09296$	$8.08789$	$[0, 1, 0, -15140165, -22679876749]$	\(y^2=x^3+x^2-15140165x-22679876749\)	5.12.0.a.2, 20.24.0-5.a.2.4, 22.2.0.a.1, 25.60.0.a.2, 100.120.0.?, $\ldots$	$[(76910076374/445, 21328167502260157/445)]$	$1$
1936.i2	1936g2	1936.i	1936g	$3$	$25$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{11} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.60.0.1	5Cs.4.1	$1100$	$1200$	$37$	$4.414860402$	$1$		$0$	$4800$	$1.584085$	$-122023936/161051$	$1.01300$	$5.61718$	$[0, 1, 0, -20005, -1979309]$	\(y^2=x^3+x^2-20005x-1979309\)	5.60.0.a.1, 20.120.0-5.a.1.4, 22.2.0.a.1, 110.120.5.?, 220.240.5.?, $\ldots$	$[(15894/5, 1947253/5)]$	$1$
1936.i3	1936g1	1936.i	1936g	$3$	$25$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.1	5B.4.1	$1100$	$1200$	$37$	$0.882972080$	$1$		$2$	$960$	$0.779366$	$-4096/11$	$0.82546$	$4.32760$	$[0, 1, 0, -645, 14771]$	\(y^2=x^3+x^2-645x+14771\)	5.12.0.a.1, 20.24.0-5.a.1.4, 22.2.0.a.1, 25.60.0.a.1, 100.120.0.?, $\ldots$	$[(-26, 121)]$	$1$
1936.j1	1936j2	1936.j	1936j	$2$	$3$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{24} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.4.0.2, 3.4.0.1	3B	$24$	$32$	$0$	$1.270567264$	$1$		$2$	$12672$	$1.760887$	$-128667913/4096$	$0.98675$	$6.10794$	$[0, -1, 0, -100712, 12669296]$	\(y^2=x^3-x^2-100712x+12669296\)	3.4.0.a.1, 4.2.0.a.1, 6.8.0-3.a.1.2, 8.4.0-4.a.1.1, 12.16.0-12.a.1.2, $\ldots$	$[(202, 726)]$	$1$
1936.j2	1936j1	1936.j	1936j	$2$	$3$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{16} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.4.0.2, 3.4.0.1	3B	$24$	$32$	$0$	$3.811701794$	$1$		$2$	$4224$	$1.211580$	$24167/16$	$0.94416$	$4.96720$	$[0, -1, 0, 5768, 62064]$	\(y^2=x^3-x^2+5768x+62064\)	3.4.0.a.1, 4.2.0.a.1, 6.8.0-3.a.1.1, 8.4.0-4.a.1.1, 12.16.0-12.a.1.4, $\ldots$	$[(18, 414)]$	$1$
1936.k1	1936i2	1936.k	1936i	$2$	$3$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{24} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$264$	$32$	$0$	$3.974153107$	$1$		$2$	$1152$	$0.561939$	$-128667913/4096$	$0.98675$	$4.20696$	$[0, -1, 0, -832, -9216]$	\(y^2=x^3-x^2-832x-9216\)	3.4.0.a.1, 4.2.0.a.1, 12.8.0.a.1, 24.16.0.b.2, 66.8.0-3.a.1.2, $\ldots$	$[(90, 798)]$	$1$
1936.k2	1936i1	1936.k	1936i	$2$	$3$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{16} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$264$	$32$	$0$	$1.324717702$	$1$		$2$	$384$	$0.012633$	$24167/16$	$0.94416$	$3.06622$	$[0, -1, 0, 48, -64]$	\(y^2=x^3-x^2+48x-64\)	3.4.0.a.1, 4.2.0.a.1, 12.8.0.a.1, 24.16.0.b.1, 66.8.0-3.a.1.1, $\ldots$	$[(2, 6)]$	$1$
1936.l1	1936e1	1936.l	1936e	$1$	$1$	\( 2^{4} \cdot 11^{2} \)	\( - 2^{8} \cdot 11^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$1920$	$0.569736$	$-27648/11$	$0.78666$	$4.05412$	$[0, 0, 0, -484, 5324]$	\(y^2=x^3-484x+5324\)	22.2.0.a.1	$[ ]$	$1$

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