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.k2	4290k3	4290.k	4290k	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 11^{4} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$1144$	$48$	$0$	$1.110547189$	$1$		$6$	$6144$	$1.018011$	$2489411558640889/1338278906250$	$0.96902$	$4.23848$	$[1, 0, 1, -2824, -15628]$	\(y^2+xy+y=x^3-2824x-15628\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 52.12.0-4.c.1.1, 88.24.0.?, $\ldots$	$[(-20, 191)]$
12870.by2	12870bx4	12870.by	12870bx	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{8} \cdot 11^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$1$	$1$		$0$	$49152$	$1.567318$	$2489411558640889/1338278906250$	$0.96902$	$4.44299$	$[1, -1, 1, -25412, 421949]$	\(y^2+xy+y=x^3-x^2-25412x+421949\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
21450.bx2	21450bx3	21450.bx	21450bx	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{14} \cdot 11^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5720$	$48$	$0$	$1$	$1$		$0$	$147456$	$1.822731$	$2489411558640889/1338278906250$	$0.96902$	$4.52274$	$[1, 1, 1, -70588, -1953469]$	\(y^2+xy+y=x^3+x^2-70588x-1953469\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
34320.e2	34320z3	34320.e	34320z	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{13} \cdot 3^{2} \cdot 5^{8} \cdot 11^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1144$	$48$	$0$	$1$	$1$		$1$	$147456$	$1.711159$	$2489411558640889/1338278906250$	$0.96902$	$4.19100$	$[0, -1, 0, -45176, 1000176]$	\(y^2=x^3-x^2-45176x+1000176\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 52.12.0-4.c.1.2, 88.24.0.?, $\ldots$	$[ ]$
47190.cm2	47190cm3	47190.cm	47190cm	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 11^{10} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1144$	$48$	$0$	$12.15588999$	$1$		$0$	$737280$	$2.216961$	$2489411558640889/1338278906250$	$0.96902$	$4.63097$	$[1, 0, 0, -341646, 20458890]$	\(y^2+xy=x^3-341646x+20458890\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 88.24.0.?, 104.24.0.?, $\ldots$	$[(6772467/82, 14293310103/82)]$
55770.da2	55770cx3	55770.da	55770cx	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 11^{4} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1144$	$48$	$0$	$1$	$1$		$0$	$1032192$	$2.300488$	$2489411558640889/1338278906250$	$0.96902$	$4.65189$	$[1, 0, 0, -477175, -33856993]$	\(y^2+xy=x^3-477175x-33856993\)	2.3.0.a.1, 4.12.0-4.c.1.2, 88.24.0.?, 104.24.0.?, 1144.48.0.?	$[ ]$
64350.bg2	64350bd3	64350.bg	64350bd	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{14} \cdot 11^{4} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$17160$	$48$	$0$	$5.560615010$	$1$		$0$	$1179648$	$2.372036$	$2489411558640889/1338278906250$	$0.96902$	$4.66932$	$[1, -1, 0, -635292, 52108366]$	\(y^2+xy=x^3-x^2-635292x+52108366\)	2.3.0.a.1, 4.6.0.c.1, 88.12.0.?, 104.12.0.?, 120.12.0.?, $\ldots$	$[(7367/2, 565447/2)]$
102960.do2	102960ei3	102960.do	102960ei	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{13} \cdot 3^{8} \cdot 5^{8} \cdot 11^{4} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$0.601922388$	$1$		$9$	$1179648$	$2.260464$	$2489411558640889/1338278906250$	$0.96902$	$4.36318$	$[0, 0, 0, -406587, -26598166]$	\(y^2=x^3-406587x-26598166\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 88.12.0.?, 104.12.0.?, $\ldots$	$[(773, 11000)]$
137280.cs2	137280gd4	137280.cs	137280gd	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{19} \cdot 3^{2} \cdot 5^{8} \cdot 11^{4} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1144$	$48$	$0$	$0.860222293$	$1$		$7$	$1179648$	$2.057732$	$2489411558640889/1338278906250$	$0.96902$	$4.05143$	$[0, -1, 0, -180705, -7820703]$	\(y^2=x^3-x^2-180705x-7820703\)	2.3.0.a.1, 4.12.0-4.c.1.2, 88.24.0.?, 104.24.0.?, 1144.48.0.?	$[(-151, 4000)]$
137280.gr2	137280g3	137280.gr	137280g	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{19} \cdot 3^{2} \cdot 5^{8} \cdot 11^{4} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1144$	$48$	$0$	$1$	$1$		$3$	$1179648$	$2.057732$	$2489411558640889/1338278906250$	$0.96902$	$4.05143$	$[0, 1, 0, -180705, 7820703]$	\(y^2=x^3+x^2-180705x+7820703\)	2.3.0.a.1, 4.12.0-4.c.1.1, 88.24.0.?, 104.24.0.?, 1144.48.0.?	$[ ]$
141570.cd2	141570db4	141570.cd	141570db	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{8} \cdot 11^{10} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$3.150852499$	$1$		$4$	$5898240$	$2.766266$	$2489411558640889/1338278906250$	$0.96902$	$4.75778$	$[1, -1, 0, -3074814, -552390030]$	\(y^2+xy=x^3-x^2-3074814x-552390030\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 88.12.0.?, 104.12.0.?, $\ldots$	$[(-249, 14187)]$
167310.r2	167310ei3	167310.r	167310ei	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2 \cdot 3^{8} \cdot 5^{8} \cdot 11^{4} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$2.618026431$	$1$		$2$	$8257536$	$2.849792$	$2489411558640889/1338278906250$	$0.96902$	$4.77503$	$[1, -1, 0, -4294575, 914138811]$	\(y^2+xy=x^3-x^2-4294575x+914138811\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[(205, 6404)]$
171600.ft2	171600bt3	171600.ft	171600bt	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{13} \cdot 3^{2} \cdot 5^{14} \cdot 11^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5720$	$48$	$0$	$1$	$1$		$1$	$3538944$	$2.515877$	$2489411558640889/1338278906250$	$0.96902$	$4.43255$	$[0, 1, 0, -1129408, 122763188]$	\(y^2=x^3+x^2-1129408x+122763188\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.2, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
210210.bf2	210210ej3	210210.bf	210210ej	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 7^{6} \cdot 11^{4} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$8008$	$48$	$0$	$0.579945685$	$1$		$8$	$2359296$	$1.990967$	$2489411558640889/1338278906250$	$0.96902$	$3.84520$	$[1, 1, 0, -138352, 5221966]$	\(y^2+xy=x^3+x^2-138352x+5221966\)	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.2, 88.12.0.?, 104.12.0.?, $\ldots$	$[(7, 2059)]$
235950.bb2	235950bb3	235950.bb	235950bb	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{14} \cdot 11^{10} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5720$	$48$	$0$	$1$	$1$		$0$	$17694720$	$3.021679$	$2489411558640889/1338278906250$	$0.96902$	$4.80907$	$[1, 1, 0, -8541150, 2557361250]$	\(y^2+xy=x^3+x^2-8541150x+2557361250\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
278850.z2	278850z4	278850.z	278850z	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13^{2} \)	\( 2 \cdot 3^{2} \cdot 5^{14} \cdot 11^{4} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5720$	$48$	$0$	$5.985504292$	$1$		$2$	$24772608$	$3.105206$	$2489411558640889/1338278906250$	$0.96902$	$4.82494$	$[1, 1, 0, -11929375, -4232124125]$	\(y^2+xy=x^3+x^2-11929375x-4232124125\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[(-2989, 70283)]$
377520.w2	377520w4	377520.w	377520w	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{13} \cdot 3^{2} \cdot 5^{8} \cdot 11^{10} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1144$	$48$	$0$	$1$	$1$		$1$	$17694720$	$2.910107$	$2489411558640889/1338278906250$	$0.96902$	$4.52879$	$[0, -1, 0, -5466336, -1309368960]$	\(y^2=x^3-x^2-5466336x-1309368960\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 88.24.0.?, 104.24.0.?, $\ldots$	$[ ]$
411840.dh2	411840dh4	411840.dh	411840dh	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{19} \cdot 3^{8} \cdot 5^{8} \cdot 11^{4} \cdot 13 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$26.12167449$	$1$		$5$	$9437184$	$2.607040$	$2489411558640889/1338278906250$	$0.96902$	$4.21701$	$[0, 0, 0, -1626348, -212785328]$	\(y^2=x^3-1626348x-212785328\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 88.12.0.?, 104.12.0.?, $\ldots$	$[(-579, 23125), (-6384/5, 1704164/5)]$
411840.du2	411840du3	411840.du	411840du	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{19} \cdot 3^{8} \cdot 5^{8} \cdot 11^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$1$	$1$		$1$	$9437184$	$2.607040$	$2489411558640889/1338278906250$	$0.96902$	$4.21701$	$[0, 0, 0, -1626348, 212785328]$	\(y^2=x^3-1626348x+212785328\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
446160.di2	446160di3	446160.di	446160di	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{13} \cdot 3^{2} \cdot 5^{8} \cdot 11^{4} \cdot 13^{7} \)	$2$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1144$	$48$	$0$	$2.355349350$	$1$		$31$	$24772608$	$2.993633$	$2489411558640889/1338278906250$	$0.96902$	$4.54769$	$[0, -1, 0, -7634800, 2166847552]$	\(y^2=x^3-x^2-7634800x+2166847552\)	2.3.0.a.1, 4.12.0-4.c.1.1, 88.24.0.?, 104.24.0.?, 1144.48.0.?	$[(-416, 72600), (-2656, 60840)]$

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