Elliptic curves over Q\Q of conductor 28749

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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
28749.a1	28749a4	28749.a	28749a	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$3^{4} \cdot 7^{4} \cdot 37^{7}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$6216$	$48$	$0$	$3.540481725$	$1$		$0$	$262656$	$1.951990$	$974126411497/7195797$	$0.90966$	$4.79920$	$[1, 1, 1, -282727, -57610072]$	$y^2+xy+y=x^3+x^2-282727x-57610072$	2.3.0.a.1, 4.12.0-4.c.1.2, 74.6.0.?, 148.24.0.?, 168.24.0.?, $\ldots$	$[(19264/3, 2553709/3)]$
28749.a2	28749a2	28749.a	28749a	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$3^{2} \cdot 7^{2} \cdot 37^{8}$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3108$	$48$	$0$	$7.080963451$	$1$		$2$	$131328$	$1.605417$	$1102302937/603729$	$0.89606$	$4.13839$	$[1, 1, 1, -29462, 438266]$	$y^2+xy+y=x^3+x^2-29462x+438266$	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 148.24.0.?, 3108.48.0.?	$[(-2166/5, 196967/5)]$
28749.a3	28749a1	28749.a	28749a	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$3 \cdot 7 \cdot 37^{7}$	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$6216$	$48$	$0$	$14.16192690$	$1$		$3$	$65664$	$1.258844$	$498677257/777$	$0.83320$	$4.06113$	$[1, 1, 1, -22617, 1297998]$	$y^2+xy+y=x^3+x^2-22617x+1297998$	2.3.0.a.1, 4.12.0-4.c.1.1, 168.24.0.?, 296.24.0.?, 1554.6.0.?, $\ldots$	$[(1736386/105, 1405875101/105)]$
28749.a4	28749a3	28749.a	28749a	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$- 3 \cdot 7 \cdot 37^{10}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$6216$	$48$	$0$	$3.540481725$	$4$	$2$	$2$	$262656$	$1.951990$	$64336588343/39357381$	$0.93572$	$4.53451$	$[1, 1, 1, 114283, 3600656]$	$y^2+xy+y=x^3+x^2+114283x+3600656$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 148.12.0.?, $\ldots$	$[(1088, 37103)]$
28749.b1	28749f4	28749.b	28749f	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$3^{20} \cdot 7 \cdot 37^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6216$	$48$	$0$	$1$	$1$		$0$	$1313280$	$2.794403$	$1969718647361977/903077159859$	$1.02671$	$5.54064$	$[1, 0, 0, -3575172, 1185634485]$	$y^2+xy=x^3-3575172x+1185634485$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 28.12.0-4.c.1.1, 148.12.0.?, $\ldots$	$[]$
28749.b2	28749f2	28749.b	28749f	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$3^{10} \cdot 7^{2} \cdot 37^{8}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3108$	$48$	$0$	$1$	$4$	$2$	$2$	$656640$	$2.447830$	$252352098250057/3961065969$	$0.99405$	$5.34049$	$[1, 0, 0, -1802317, -918744400]$	$y^2+xy=x^3-1802317x-918744400$	2.6.0.a.1, 12.12.0.b.1, 28.12.0-2.a.1.1, 84.24.0.?, 148.12.0.?, $\ldots$	$[]$
28749.b3	28749f1	28749.b	28749f	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$3^{5} \cdot 7 \cdot 37^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6216$	$48$	$0$	$1$	$4$	$2$	$1$	$328320$	$2.101254$	$249487788397177/62937$	$0.94786$	$5.33938$	$[1, 0, 0, -1795472, -926160273]$	$y^2+xy=x^3-1795472x-926160273$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 28.12.0-4.c.1.2, 168.24.0.?, $\ldots$	$[]$
28749.b4	28749f3	28749.b	28749f	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$- 3^{5} \cdot 7^{4} \cdot 37^{10}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6216$	$48$	$0$	$1$	$4$	$2$	$0$	$1313280$	$2.794403$	$-115714886617/1093466116323$	$1.05228$	$5.53659$	$[1, 0, 0, -138982, -2548480033]$	$y^2+xy=x^3-138982x-2548480033$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 12.12.0.g.1, 56.12.0-4.c.1.5, $\ldots$	$[]$
28749.c1	28749c1	28749.c	28749c	$1$	$1$	$3 \cdot 7 \cdot 37^{2}$	$- 3^{4} \cdot 7 \cdot 37^{7}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$518$	$2$	$0$	$1$	$1$		$0$	$131328$	$1.718983$	$-536971313152/20979$	$0.96750$	$4.74119$	$[0, -1, 1, -231817, -42884445]$	$y^2+y=x^3-x^2-231817x-42884445$	518.2.0.?	$[]$
28749.d1	28749j1	28749.d	28749j	$1$	$1$	$3 \cdot 7 \cdot 37^{2}$	$3^{5} \cdot 7 \cdot 37^{2}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$42$	$2$	$0$	$0.406374590$	$1$		$4$	$5040$	$-0.058485$	$9699328/1701$	$1.03521$	$2.27046$	$[0, 1, 1, -49, -128]$	$y^2+y=x^3+x^2-49x-128$	42.2.0.a.1	$[(-4, 4)]$
28749.e1	28749h1	28749.e	28749h	$1$	$1$	$3 \cdot 7 \cdot 37^{2}$	$- 3^{4} \cdot 7^{5} \cdot 37^{7}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$518$	$2$	$0$	$0.646783467$	$1$		$4$	$218880$	$1.962408$	$71991296/50370579$	$1.02948$	$4.56387$	$[0, 1, 1, 11865, 17293043]$	$y^2+y=x^3+x^2+11865x+17293043$	518.2.0.?	$[(567, 14374)]$
28749.f1	28749i1	28749.f	28749i	$1$	$1$	$3 \cdot 7 \cdot 37^{2}$	$3^{5} \cdot 7 \cdot 37^{8}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$42$	$2$	$0$	$4.431990129$	$1$		$2$	$186480$	$1.746973$	$9699328/1701$	$1.03521$	$4.38080$	$[0, 1, 1, -67537, -5662349]$	$y^2+y=x^3+x^2-67537x-5662349$	42.2.0.a.1	$[(-115, 772)]$
28749.g1	28749d4	28749.g	28749d	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$3 \cdot 7 \cdot 37^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6216$	$48$	$0$	$1$	$4$	$2$	$0$	$437760$	$2.236973$	$7870267657034497/777$	$1.03732$	$5.67556$	$[1, 1, 0, -5673164, 5198628123]$	$y^2+xy=x^3+x^2-5673164x+5198628123$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 56.12.0.ba.1, 168.24.0.?, $\ldots$	$[]$
28749.g2	28749d3	28749.g	28749d	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$3^{4} \cdot 7 \cdot 37^{10}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6216$	$48$	$0$	$1$	$4$	$2$	$0$	$437760$	$2.236973$	$2810981740897/1062649287$	$0.93351$	$4.90243$	$[1, 1, 0, -402514, 57712777]$	$y^2+xy=x^3+x^2-402514x+57712777$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0.h.1, 148.12.0.?, $\ldots$	$[]$
28749.g3	28749d2	28749.g	28749d	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$3^{2} \cdot 7^{2} \cdot 37^{8}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3108$	$48$	$0$	$1$	$4$	$2$	$2$	$218880$	$1.890398$	$1921886786737/603729$	$0.91480$	$4.86539$	$[1, 1, 0, -354599, 81104880]$	$y^2+xy=x^3+x^2-354599x+81104880$	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0.a.1, 84.24.0.?, 148.12.0.?, $\ldots$	$[]$
28749.g4	28749d1	28749.g	28749d	$4$	$4$	$3 \cdot 7 \cdot 37^{2}$	$- 3 \cdot 7^{4} \cdot 37^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6216$	$48$	$0$	$1$	$1$		$1$	$109440$	$1.543823$	$-304821217/266511$	$0.84920$	$4.10285$	$[1, 1, 0, -19194, 1613895]$	$y^2+xy=x^3+x^2-19194x+1613895$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0.ba.1, 148.12.0.?, $\ldots$	$[]$
28749.h1	28749e6	28749.h	28749e	$6$	$8$	$3 \cdot 7 \cdot 37^{2}$	$3 \cdot 7^{2} \cdot 37^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$12432$	$192$	$1$	$1$	$16$	$2$	$0$	$202752$	$1.879663$	$53297461115137/147$	$1.05087$	$5.18903$	$[1, 0, 1, -1073325, -428090351]$	$y^2+xy+y=x^3-1073325x-428090351$	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, $\ldots$	$[]$
28749.h2	28749e4	28749.h	28749e	$6$	$8$	$3 \cdot 7 \cdot 37^{2}$	$3^{2} \cdot 7^{4} \cdot 37^{6}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.18	2Cs	$6216$	$192$	$1$	$1$	$16$	$2$	$2$	$101376$	$1.533091$	$13027640977/21609$	$1.08149$	$4.37895$	$[1, 0, 1, -67110, -6687509]$	$y^2+xy+y=x^3-67110x-6687509$	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, $\ldots$	$[]$
28749.h3	28749e3	28749.h	28749e	$6$	$8$	$3 \cdot 7 \cdot 37^{2}$	$3^{8} \cdot 7 \cdot 37^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$12432$	$192$	$1$	$1$	$1$		$0$	$101376$	$1.533091$	$6570725617/45927$	$1.00160$	$4.31228$	$[1, 0, 1, -53420, 4718999]$	$y^2+xy+y=x^3-53420x+4718999$	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, $\ldots$	$[]$
28749.h4	28749e5	28749.h	28749e	$6$	$8$	$3 \cdot 7 \cdot 37^{2}$	$- 3 \cdot 7^{8} \cdot 37^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$12432$	$192$	$1$	$1$	$16$	$2$	$0$	$202752$	$1.879663$	$-4354703137/17294403$	$1.04266$	$4.47307$	$[1, 0, 1, -46575, -10852007]$	$y^2+xy+y=x^3-46575x-10852007$	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, $\ldots$	$[]$
28749.h5	28749e2	28749.h	28749e	$6$	$8$	$3 \cdot 7 \cdot 37^{2}$	$3^{4} \cdot 7^{2} \cdot 37^{6}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.10	2Cs	$6216$	$192$	$1$	$1$	$4$	$2$	$2$	$50688$	$1.186518$	$7189057/3969$	$1.14862$	$3.64819$	$[1, 0, 1, -5505, -34169]$	$y^2+xy+y=x^3-5505x-34169$	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, $\ldots$	$[]$
28749.h6	28749e1	28749.h	28749e	$6$	$8$	$3 \cdot 7 \cdot 37^{2}$	$- 3^{2} \cdot 7 \cdot 37^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.1	2B	$12432$	$192$	$1$	$1$	$4$	$2$	$1$	$25344$	$0.839944$	$103823/63$	$0.97868$	$3.23542$	$[1, 0, 1, 1340, -4051]$	$y^2+xy+y=x^3+1340x-4051$	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, $\ldots$	$[]$
28749.i1	28749b1	28749.i	28749b	$1$	$1$	$3 \cdot 7 \cdot 37^{2}$	$- 3^{10} \cdot 7^{13} \cdot 37^{7}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$518$	$2$	$0$	$19.58539747$	$1$		$0$	$29877120$	$4.155617$	$-1795102530323910983888896/211684369494348891$	$1.05409$	$7.55018$	$[0, -1, 1, -3466240006, 78557325749583]$	$y^2+y=x^3-x^2-3466240006x+78557325749583$	518.2.0.?	$[(1735106436301/7066, 91574185287575083/7066)]$
28749.j1	28749g1	28749.j	28749g	$1$	$1$	$3 \cdot 7 \cdot 37^{2}$	$- 3^{2} \cdot 7 \cdot 37^{7}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$518$	$2$	$0$	$1$	$1$		$0$	$65664$	$1.130713$	$-4096/2331$	$0.85839$	$3.59186$	$[0, 1, 1, -456, 117569]$	$y^2+y=x^3+x^2-456x+117569$	518.2.0.?	$[]$

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