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.k1	4290k4	4290.k	4290k	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.8	2B	$1144$	$48$	$0$	$1.110547189$	$1$		$4$	$6144$	$1.018011$	$2035678735521204409/141376950$	$1.01464$	$5.04031$	$[1, 0, 1, -26404, 1649156]$	\(y^2+xy+y=x^3-26404x+1649156\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 44.12.0-4.c.1.1, 88.24.0.?, $\ldots$	$[(94, -43)]$
12870.by1	12870bx3	12870.by	12870bx	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{2} \cdot 11 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$1$	$4$	$2$	$0$	$49152$	$1.567318$	$2035678735521204409/141376950$	$1.01464$	$5.15173$	$[1, -1, 1, -237632, -44527219]$	\(y^2+xy+y=x^3-x^2-237632x-44527219\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
21450.bx1	21450bx4	21450.bx	21450bx	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 11 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5720$	$48$	$0$	$1$	$1$		$0$	$147456$	$1.822731$	$2035678735521204409/141376950$	$1.01464$	$5.19518$	$[1, 1, 1, -660088, 206144531]$	\(y^2+xy+y=x^3+x^2-660088x+206144531\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.2, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
34320.e1	34320z4	34320.e	34320z	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{13} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1144$	$48$	$0$	$1$	$1$		$1$	$147456$	$1.711159$	$2035678735521204409/141376950$	$1.01464$	$4.83317$	$[0, -1, 0, -422456, -105546000]$	\(y^2=x^3-x^2-422456x-105546000\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 44.12.0-4.c.1.2, 88.24.0.?, $\ldots$	$[ ]$
47190.cm1	47190cm4	47190.cm	47190cm	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11^{7} \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1144$	$48$	$0$	$12.15588999$	$1$		$0$	$737280$	$2.216961$	$2035678735521204409/141376950$	$1.01464$	$5.25414$	$[1, 0, 0, -3194826, -2198221794]$	\(y^2+xy=x^3-3194826x-2198221794\)	2.3.0.a.1, 4.12.0-4.c.1.2, 88.24.0.?, 104.24.0.?, 1144.48.0.?	$[(226251/10, 45305919/10)]$
55770.da1	55770cx4	55770.da	55770cx	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1144$	$48$	$0$	$1$	$4$	$2$	$0$	$1032192$	$2.300488$	$2035678735521204409/141376950$	$1.01464$	$5.26554$	$[1, 0, 0, -4462195, 3627658475]$	\(y^2+xy=x^3-4462195x+3627658475\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 88.24.0.?, 104.24.0.?, $\ldots$	$[ ]$
64350.bg1	64350bd4	64350.bg	64350bd	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{8} \cdot 11 \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$17160$	$48$	$0$	$5.560615010$	$1$		$0$	$1179648$	$2.372036$	$2035678735521204409/141376950$	$1.01464$	$5.27503$	$[1, -1, 0, -5940792, -5571843134]$	\(y^2+xy=x^3-x^2-5940792x-5571843134\)	2.3.0.a.1, 4.6.0.c.1, 88.12.0.?, 104.12.0.?, 120.12.0.?, $\ldots$	$[(11271/2, 47879/2)]$
102960.do1	102960ei4	102960.do	102960ei	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{13} \cdot 3^{8} \cdot 5^{2} \cdot 11 \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$2.407689554$	$1$		$5$	$1179648$	$2.260464$	$2035678735521204409/141376950$	$1.01464$	$4.94423$	$[0, 0, 0, -3802107, 2853544106]$	\(y^2=x^3-3802107x+2853544106\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[(1127, 70)]$
137280.cs1	137280gd3	137280.cs	137280gd	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{19} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1144$	$48$	$0$	$3.440889175$	$1$		$7$	$1179648$	$2.057732$	$2035678735521204409/141376950$	$1.01464$	$4.61835$	$[0, -1, 0, -1689825, 846057825]$	\(y^2=x^3-x^2-1689825x+846057825\)	2.3.0.a.1, 4.12.0-4.c.1.1, 88.24.0.?, 104.24.0.?, 1144.48.0.?	$[(760, 435)]$
137280.gr1	137280g4	137280.gr	137280g	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{19} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1144$	$48$	$0$	$1$	$4$	$2$	$1$	$1179648$	$2.057732$	$2035678735521204409/141376950$	$1.01464$	$4.61835$	$[0, 1, 0, -1689825, -846057825]$	\(y^2=x^3+x^2-1689825x-846057825\)	2.3.0.a.1, 4.12.0-4.c.1.2, 88.24.0.?, 104.24.0.?, 1144.48.0.?	$[ ]$
141570.cd1	141570db3	141570.cd	141570db	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{2} \cdot 11^{7} \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$0.787713124$	$1$		$8$	$5898240$	$2.766266$	$2035678735521204409/141376950$	$1.01464$	$5.32323$	$[1, -1, 0, -28753434, 59351988438]$	\(y^2+xy=x^3-x^2-28753434x+59351988438\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[(3087, -666)]$
167310.r1	167310ei4	167310.r	167310ei	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2 \cdot 3^{8} \cdot 5^{2} \cdot 11 \cdot 13^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$10.47210572$	$1$		$2$	$8257536$	$2.849792$	$2035678735521204409/141376950$	$1.01464$	$5.33263$	$[1, -1, 0, -40159755, -97946778825]$	\(y^2+xy=x^3-x^2-40159755x-97946778825\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 88.12.0.?, 104.12.0.?, $\ldots$	$[(102291, 32600085)]$
171600.ft1	171600bt4	171600.ft	171600bt	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{13} \cdot 3^{2} \cdot 5^{8} \cdot 11 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5720$	$48$	$0$	$1$	$4$	$2$	$1$	$3538944$	$2.515877$	$2035678735521204409/141376950$	$1.01464$	$4.98898$	$[0, 1, 0, -10561408, -13214372812]$	\(y^2=x^3+x^2-10561408x-13214372812\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
210210.bf1	210210ej4	210210.bf	210210ej	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 11 \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$8008$	$48$	$0$	$2.319782740$	$1$		$6$	$2359296$	$1.990967$	$2035678735521204409/141376950$	$1.01464$	$4.39241$	$[1, 1, 0, -1293772, -566954366]$	\(y^2+xy=x^3+x^2-1293772x-566954366\)	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[(-657, 331)]$
235950.bb1	235950bb4	235950.bb	235950bb	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 11^{7} \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5720$	$48$	$0$	$1$	$4$	$2$	$0$	$17694720$	$3.021679$	$2035678735521204409/141376950$	$1.01464$	$5.35117$	$[1, 1, 0, -79870650, -274777724250]$	\(y^2+xy=x^3+x^2-79870650x-274777724250\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
278850.z1	278850z3	278850.z	278850z	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13^{2} \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 11 \cdot 13^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5720$	$48$	$0$	$5.985504292$	$1$		$2$	$24772608$	$3.105206$	$2035678735521204409/141376950$	$1.01464$	$5.35982$	$[1, 1, 0, -111554875, 453457309375]$	\(y^2+xy=x^3+x^2-111554875x+453457309375\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 88.12.0.?, 104.12.0.?, $\ldots$	$[(70361, 18429506)]$
377520.w1	377520w3	377520.w	377520w	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{13} \cdot 3^{2} \cdot 5^{2} \cdot 11^{7} \cdot 13^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1144$	$48$	$0$	$1$	$1$		$3$	$17694720$	$2.910107$	$2035678735521204409/141376950$	$1.01464$	$5.05105$	$[0, -1, 0, -51117216, 140686194816]$	\(y^2=x^3-x^2-51117216x+140686194816\)	2.3.0.a.1, 4.12.0-4.c.1.1, 88.24.0.?, 104.24.0.?, 1144.48.0.?	$[ ]$
411840.dh1	411840dh3	411840.dh	411840dh	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{19} \cdot 3^{8} \cdot 5^{2} \cdot 11 \cdot 13^{4} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$1.632604656$	$1$		$21$	$9437184$	$2.607040$	$2035678735521204409/141376950$	$1.01464$	$4.73575$	$[0, 0, 0, -15208428, 22828352848]$	\(y^2=x^3-15208428x+22828352848\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 88.12.0.?, 104.12.0.?, $\ldots$	$[(2234, 1440), (6074, 393120)]$
411840.du1	411840du4	411840.du	411840du	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{19} \cdot 3^{8} \cdot 5^{2} \cdot 11 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$1$	$1$		$1$	$9437184$	$2.607040$	$2035678735521204409/141376950$	$1.01464$	$4.73575$	$[0, 0, 0, -15208428, -22828352848]$	\(y^2=x^3-15208428x-22828352848\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 88.12.0.?, 104.12.0.?, $\ldots$	$[ ]$
446160.di1	446160di4	446160.di	446160di	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{13} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13^{10} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1144$	$48$	$0$	$37.68558960$	$1$		$7$	$24772608$	$2.993633$	$2035678735521204409/141376950$	$1.01464$	$5.06324$	$[0, -1, 0, -71395120, -232170142400]$	\(y^2=x^3-x^2-71395120x-232170142400\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 88.24.0.?, 104.24.0.?, $\ldots$	$[(-4878, 118), (18530, 2192490)]$

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