Elliptic curve search results

Results (20 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	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
4290.bc2	4290bc3	4290.bc	4290bc	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{4} \cdot 11^{2} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.31	2Cs	$17160$	$192$	$1$	$1$	$1$		$2$	$30720$	$1.704388$	$5683972151443376419201/1244117160000$	$0.99969$	$5.98896$	$[1, 0, 0, -371800, -87290368]$	\(y^2+xy=x^3-371800x-87290368\)	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.d.1.2, 264.96.0.?, 520.96.0.?, $\ldots$	$[ ]$
12870.f2	12870k3	12870.f	12870k	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{6} \cdot 3^{8} \cdot 5^{4} \cdot 11^{2} \cdot 13^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$1.001963354$	$1$		$10$	$245760$	$2.253693$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99024$	$[1, -1, 0, -3346200, 2356839936]$	\(y^2+xy=x^3-x^2-3346200x+2356839936\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 12.24.0-4.b.1.1, 24.48.0-8.d.1.1, $\ldots$	$[(1047, 3)]$
21450.k2	21450f4	21450.k	21450f	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{10} \cdot 11^{2} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$1$	$4$	$2$	$2$	$737280$	$2.509106$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99074$	$[1, 1, 0, -9295000, -10911296000]$	\(y^2+xy=x^3+x^2-9295000x-10911296000\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 20.24.0-4.b.1.1, 40.48.0-8.d.1.2, $\ldots$	$[ ]$
34320.u2	34320bh4	34320.u	34320bh	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{4} \cdot 11^{2} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.27	2Cs	$17160$	$192$	$1$	$1$	$1$		$7$	$737280$	$2.397533$	$5683972151443376419201/1244117160000$	$0.99969$	$5.59293$	$[0, -1, 0, -5948800, 5586583552]$	\(y^2=x^3-x^2-5948800x+5586583552\)	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.d.1.10, 264.96.0.?, 520.96.0.?, $\ldots$	$[ ]$
47190.bi2	47190bg4	47190.bi	47190bg	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{4} \cdot 11^{8} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$1$	$1$		$2$	$3686400$	$2.903336$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99142$	$[1, 0, 1, -44987803, 116138492006]$	\(y^2+xy+y=x^3-44987803x+116138492006\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 24.48.0-8.d.1.7, 44.24.0-4.b.1.1, $\ldots$	$[ ]$
55770.y2	55770u4	55770.y	55770u	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{6} \cdot 3^{2} \cdot 5^{4} \cdot 11^{2} \cdot 13^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$1$	$4$	$2$	$2$	$5160960$	$2.986862$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99155$	$[1, 0, 1, -62834204, -191714104294]$	\(y^2+xy+y=x^3-62834204x-191714104294\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 40.48.0-8.d.1.11, 52.24.0-4.b.1.1, $\ldots$	$[ ]$
64350.dr2	64350dj4	64350.dr	64350dj	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{6} \cdot 3^{8} \cdot 5^{10} \cdot 11^{2} \cdot 13^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$2.422376089$	$1$		$6$	$5898240$	$3.058411$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99166$	$[1, -1, 1, -83655005, 294521336997]$	\(y^2+xy+y=x^3-x^2-83655005x+294521336997\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 60.24.0-4.b.1.1, 120.48.0.?, $\ldots$	$[(5439, 17280)]$
102960.bl2	102960dt4	102960.bl	102960dt	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{18} \cdot 3^{8} \cdot 5^{4} \cdot 11^{2} \cdot 13^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$6.174047536$	$1$		$5$	$5898240$	$2.946842$	$5683972151443376419201/1244117160000$	$0.99969$	$5.63168$	$[0, 0, 0, -53539203, -150784216702]$	\(y^2=x^3-53539203x-150784216702\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 12.24.0-4.b.1.3, 24.48.0-8.d.1.9, $\ldots$	$[(24001, 3519936)]$
137280.n2	137280ha4	137280.n	137280ha	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{24} \cdot 3^{2} \cdot 5^{4} \cdot 11^{2} \cdot 13^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.106	2Cs	$17160$	$192$	$1$	$19.02926571$	$1$		$3$	$5898240$	$2.744106$	$5683972151443376419201/1244117160000$	$0.99969$	$5.28908$	$[0, -1, 0, -23795201, -44668873215]$	\(y^2=x^3-x^2-23795201x-44668873215\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.d.1.9, 132.24.0.?, 264.96.0.?, $\ldots$	$[(-3982343816/1189, 59295917737/1189)]$
137280.ez2	137280bg3	137280.ez	137280bg	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{24} \cdot 3^{2} \cdot 5^{4} \cdot 11^{2} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.135	2Cs	$17160$	$192$	$1$	$1$	$4$	$2$	$3$	$5898240$	$2.744106$	$5683972151443376419201/1244117160000$	$0.99969$	$5.28908$	$[0, 1, 0, -23795201, 44668873215]$	\(y^2=x^3+x^2-23795201x+44668873215\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.d.1.1, 132.24.0.?, 264.96.0.?, $\ldots$	$[ ]$
141570.dg2	141570bs4	141570.dg	141570bs	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{6} \cdot 3^{8} \cdot 5^{4} \cdot 11^{8} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.134	2Cs	$17160$	$192$	$1$	$1$	$4$	$2$	$2$	$29491200$	$3.452641$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99222$	$[1, -1, 1, -404890223, -3135739284169]$	\(y^2+xy+y=x^3-x^2-404890223x-3135739284169\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.d.1.8, 132.24.0.?, 264.96.0.?, $\ldots$	$[ ]$
167310.fe2	167310k3	167310.fe	167310k	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{6} \cdot 3^{8} \cdot 5^{4} \cdot 11^{2} \cdot 13^{10} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$2.433757809$	$1$		$8$	$41287680$	$3.536167$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99232$	$[1, -1, 1, -565507832, 5176280815931]$	\(y^2+xy+y=x^3-x^2-565507832x+5176280815931\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 120.48.0.?, 156.24.0.?, $\ldots$	$[(13791, 5479)]$
171600.fr2	171600bv3	171600.fr	171600bv	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{10} \cdot 11^{2} \cdot 13^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$6.561555502$	$1$		$5$	$17694720$	$3.202255$	$5683972151443376419201/1244117160000$	$0.99969$	$5.64729$	$[0, 1, 0, -148720008, 698025503988]$	\(y^2=x^3+x^2-148720008x+698025503988\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 20.24.0-4.b.1.3, 40.48.0-8.d.1.10, $\ldots$	$[(35604, 6366906)]$
210210.cx2	210210cr3	210210.cx	210210cr	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{4} \cdot 7^{6} \cdot 11^{2} \cdot 13^{4} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$120120$	$192$	$1$	$2.713812628$	$1$		$28$	$11796480$	$2.677341$	$5683972151443376419201/1244117160000$	$0.99969$	$5.03982$	$[1, 1, 1, -18218201, 29922378023]$	\(y^2+xy+y=x^3+x^2-18218201x+29922378023\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 28.24.0-4.b.1.1, 56.48.0-8.d.1.1, $\ldots$	$[(2421, 2464), (2477, -112)]$
235950.fs2	235950fs3	235950.fs	235950fs	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{10} \cdot 11^{8} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$1$	$1$		$2$	$88473600$	$3.708054$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99254$	$[1, 1, 1, -1124695063, 14517311500781]$	\(y^2+xy+y=x^3+x^2-1124695063x+14517311500781\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 120.48.0.?, 220.24.0.?, $\ldots$	$[ ]$
278850.fs2	278850fs4	278850.fs	278850fs	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13^{2} \)	\( 2^{6} \cdot 3^{2} \cdot 5^{10} \cdot 11^{2} \cdot 13^{10} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.125	2Cs	$17160$	$192$	$1$	$32.83000657$	$1$		$12$	$123863040$	$3.791580$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99264$	$[1, 1, 1, -1570855088, -23964263036719]$	\(y^2+xy+y=x^3+x^2-1570855088x-23964263036719\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.d.1.12, 260.24.0.?, 264.96.0.?, $\ldots$	$[(-22879, 9605), (326981, 185368765)]$
377520.cn2	377520cn4	377520.cn	377520cn	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{4} \cdot 11^{8} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$1$	$1$		$3$	$88473600$	$3.596481$	$5683972151443376419201/1244117160000$	$0.99969$	$5.66895$	$[0, -1, 0, -719804840, -7432863488400]$	\(y^2=x^3-x^2-719804840x-7432863488400\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 24.48.0-8.d.1.15, 44.24.0-4.b.1.3, $\ldots$	$[ ]$
411840.jr2	411840jr4	411840.jr	411840jr	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{24} \cdot 3^{8} \cdot 5^{4} \cdot 11^{2} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$1$	$1$		$3$	$47185920$	$3.293415$	$5683972151443376419201/1244117160000$	$0.99969$	$5.34949$	$[0, 0, 0, -214156812, -1206273733616]$	\(y^2=x^3-214156812x-1206273733616\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 24.48.0-8.d.1.2, 44.24.0-4.b.1.2, $\ldots$	$[ ]$
411840.km2	411840km3	411840.km	411840km	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{24} \cdot 3^{8} \cdot 5^{4} \cdot 11^{2} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$1$	$1$		$3$	$47185920$	$3.293415$	$5683972151443376419201/1244117160000$	$0.99969$	$5.34949$	$[0, 0, 0, -214156812, 1206273733616]$	\(y^2=x^3-214156812x+1206273733616\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 24.48.0-8.d.1.10, 44.24.0-4.b.1.2, $\ldots$	$[ ]$
446160.be2	446160be3	446160.be	446160be	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{18} \cdot 3^{2} \cdot 5^{4} \cdot 11^{2} \cdot 13^{10} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$8.885857929$	$1$		$3$	$123863040$	$3.680008$	$5683972151443376419201/1244117160000$	$0.99969$	$5.67320$	$[0, -1, 0, -1005347256, 12269702674800]$	\(y^2=x^3-x^2-1005347256x+12269702674800\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 40.48.0-8.d.1.3, 52.24.0-4.b.1.3, $\ldots$	$[(978562/7, 135776850/7)]$

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