Elliptic curve search results

Results (15 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	Manin constant
3243.a3	3243a2	3243.a	3243a	$4$	$4$	\( 3 \cdot 23 \cdot 47 \)	\( 3^{12} \cdot 23^{2} \cdot 47^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$4324$	$48$	$0$	$1$	$1$		$2$	$5664$	$1.122267$	$165231457514151553/621021226401$	$0.98614$	$4.90412$	$[1, 1, 1, -11432, -473704]$	\(y^2+xy+y=x^3+x^2-11432x-473704\)	2.6.0.a.1, 4.12.0-2.a.1.1, 92.24.0.?, 188.24.0.?, 4324.48.0.?	$[ ]$	$1$
9729.c3	9729b2	9729.c	9729b	$4$	$4$	\( 3^{2} \cdot 23 \cdot 47 \)	\( 3^{18} \cdot 23^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$12972$	$48$	$0$	$7.173442701$	$1$		$2$	$45312$	$1.671574$	$165231457514151553/621021226401$	$0.98614$	$5.03522$	$[1, -1, 0, -102888, 12687115]$	\(y^2+xy=x^3-x^2-102888x+12687115\)	2.6.0.a.1, 12.12.0-2.a.1.1, 92.12.0.?, 188.12.0.?, 276.24.0.?, $\ldots$	$[(105683/2, 34247713/2)]$	$1$
51888.bc3	51888v2	51888.bc	51888v	$4$	$4$	\( 2^{4} \cdot 3 \cdot 23 \cdot 47 \)	\( 2^{12} \cdot 3^{12} \cdot 23^{2} \cdot 47^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$4324$	$48$	$0$	$1$	$1$		$3$	$362496$	$1.815414$	$165231457514151553/621021226401$	$0.98614$	$4.41785$	$[0, 1, 0, -182912, 29951220]$	\(y^2=x^3+x^2-182912x+29951220\)	2.6.0.a.1, 4.12.0-2.a.1.1, 92.24.0.?, 188.24.0.?, 4324.48.0.?	$[ ]$	$1$
74589.b3	74589h2	74589.b	74589h	$4$	$4$	\( 3 \cdot 23^{2} \cdot 47 \)	\( 3^{12} \cdot 23^{8} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$4324$	$48$	$0$	$19.54717817$	$1$		$2$	$2990592$	$2.690014$	$165231457514151553/621021226401$	$0.98614$	$5.21037$	$[1, 1, 1, -6047539, 5703079016]$	\(y^2+xy+y=x^3+x^2-6047539x+5703079016\)	2.6.0.a.1, 4.12.0-2.a.1.1, 92.24.0.?, 188.24.0.?, 4324.48.0.?	$[(9629711497/2784, 212079356706613/2784)]$	$1$
81075.t3	81075t2	81075.t	81075t	$4$	$4$	\( 3 \cdot 5^{2} \cdot 23 \cdot 47 \)	\( 3^{12} \cdot 5^{6} \cdot 23^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$21620$	$48$	$0$	$4.442183039$	$1$		$2$	$724992$	$1.926987$	$165231457514151553/621021226401$	$0.98614$	$4.36187$	$[1, 0, 1, -285801, -58641377]$	\(y^2+xy+y=x^3-285801x-58641377\)	2.6.0.a.1, 20.12.0-2.a.1.1, 92.12.0.?, 188.12.0.?, 460.24.0.?, $\ldots$	$[(4343/2, 237153/2)]$	$1$
152421.c3	152421e2	152421.c	152421e	$4$	$4$	\( 3 \cdot 23 \cdot 47^{2} \)	\( 3^{12} \cdot 23^{2} \cdot 47^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$4324$	$48$	$0$	$15.99857235$	$1$		$2$	$12506112$	$3.047340$	$165231457514151553/621021226401$	$0.98614$	$5.25766$	$[1, 1, 1, -25253334, 48676285266]$	\(y^2+xy+y=x^3+x^2-25253334x+48676285266\)	2.6.0.a.1, 4.12.0-2.a.1.1, 92.24.0.?, 188.24.0.?, 4324.48.0.?	$[(-25372213/73, 97014514050/73)]$	$1$
155664.i3	155664e2	155664.i	155664e	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 23 \cdot 47 \)	\( 2^{12} \cdot 3^{18} \cdot 23^{2} \cdot 47^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$12972$	$48$	$0$	$1$	$4$	$2$	$3$	$2899968$	$2.364719$	$165231457514151553/621021226401$	$0.98614$	$4.56324$	$[0, 0, 0, -1646211, -810329150]$	\(y^2=x^3-1646211x-810329150\)	2.6.0.a.1, 12.12.0-2.a.1.1, 92.12.0.?, 188.12.0.?, 276.24.0.?, $\ldots$	$[ ]$	$1$
158907.c3	158907b2	158907.c	158907b	$4$	$4$	\( 3 \cdot 7^{2} \cdot 23 \cdot 47 \)	\( 3^{12} \cdot 7^{6} \cdot 23^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$30268$	$48$	$0$	$1.075449848$	$1$		$12$	$1631232$	$2.095222$	$165231457514151553/621021226401$	$0.98614$	$4.28534$	$[1, 0, 0, -560169, 160799904]$	\(y^2+xy=x^3-560169x+160799904\)	2.6.0.a.1, 28.12.0-2.a.1.1, 92.12.0.?, 188.12.0.?, 644.24.0.?, $\ldots$	$[(459, 432)]$	$1$
207552.l3	207552u2	207552.l	207552u	$4$	$4$	\( 2^{6} \cdot 3 \cdot 23 \cdot 47 \)	\( 2^{18} \cdot 3^{12} \cdot 23^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$8648$	$48$	$0$	$7.093813714$	$1$		$3$	$2899968$	$2.161987$	$165231457514151553/621021226401$	$0.98614$	$4.25731$	$[0, -1, 0, -731649, 240341409]$	\(y^2=x^3-x^2-731649x+240341409\)	2.6.0.a.1, 8.12.0-2.a.1.1, 92.12.0.?, 184.24.0.?, 188.12.0.?, $\ldots$	$[(6409/4, 215901/4)]$	$1$
207552.bl3	207552bl2	207552.bl	207552bl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 23 \cdot 47 \)	\( 2^{18} \cdot 3^{12} \cdot 23^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$8648$	$48$	$0$	$3.303030897$	$1$		$7$	$2899968$	$2.161987$	$165231457514151553/621021226401$	$0.98614$	$4.25731$	$[0, 1, 0, -731649, -240341409]$	\(y^2=x^3+x^2-731649x-240341409\)	2.6.0.a.1, 8.12.0-2.a.1.1, 92.12.0.?, 184.24.0.?, 188.12.0.?, $\ldots$	$[(1833, 67680)]$	$1$
223767.l3	223767l2	223767.l	223767l	$4$	$4$	\( 3^{2} \cdot 23^{2} \cdot 47 \)	\( 3^{18} \cdot 23^{8} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$12972$	$48$	$0$	$95.64404887$	$1$		$2$	$23924736$	$3.239319$	$165231457514151553/621021226401$	$0.98614$	$5.28080$	$[1, -1, 0, -54427851, -154037561288]$	\(y^2+xy=x^3-x^2-54427851x-154037561288\)	2.6.0.a.1, 12.12.0-2.a.1.1, 92.12.0.?, 188.12.0.?, 276.24.0.?, $\ldots$	$[(24785420886752674242639503119476433262921579/27206920032040338938, 119763365018083627901728624545119408552153380932140843474154560089/27206920032040338938)]$	$1$
243225.g3	243225g2	243225.g	243225g	$4$	$4$	\( 3^{2} \cdot 5^{2} \cdot 23 \cdot 47 \)	\( 3^{18} \cdot 5^{6} \cdot 23^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$64860$	$48$	$0$	$6.342897724$	$1$		$2$	$5799936$	$2.476292$	$165231457514151553/621021226401$	$0.98614$	$4.50698$	$[1, -1, 1, -2572205, 1583317172]$	\(y^2+xy+y=x^3-x^2-2572205x+1583317172\)	2.6.0.a.1, 60.12.0-2.a.1.1, 92.12.0.?, 188.12.0.?, 1380.24.0.?, $\ldots$	$[(-3729/2, 454175/2)]$	$1$
392403.v3	392403v2	392403.v	392403v	$4$	$4$	\( 3 \cdot 11^{2} \cdot 23 \cdot 47 \)	\( 3^{12} \cdot 11^{6} \cdot 23^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$47564$	$48$	$0$	$24.49747810$	$1$		$2$	$7249920$	$2.321217$	$165231457514151553/621021226401$	$0.98614$	$4.19513$	$[1, 1, 0, -1383274, 623583415]$	\(y^2+xy=x^3+x^2-1383274x+623583415\)	2.6.0.a.1, 44.12.0-2.a.1.1, 92.12.0.?, 188.12.0.?, 1012.24.0.?, $\ldots$	$[(-225249851546/17205, 181007985379042357/17205)]$	$1$
457263.l3	457263l2	457263.l	457263l	$4$	$4$	\( 3^{2} \cdot 23 \cdot 47^{2} \)	\( 3^{18} \cdot 23^{2} \cdot 47^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$12972$	$48$	$0$	$118.8205905$	$1$		$2$	$100048896$	$3.596649$	$165231457514151553/621021226401$	$0.98614$	$5.32023$	$[1, -1, 0, -227280006, -1314486982193]$	\(y^2+xy=x^3-x^2-227280006x-1314486982193\)	2.6.0.a.1, 12.12.0-2.a.1.1, 92.12.0.?, 188.12.0.?, 276.24.0.?, $\ldots$	$[(321212323914063508504221285796505711788385185930121363/641920582675285783948562, 181911515253575869789338196569840551820504080747522033355316743685838209610305837/641920582675285783948562)]$	$1$
476721.u3	476721u2	476721.u	476721u	$4$	$4$	\( 3^{2} \cdot 7^{2} \cdot 23 \cdot 47 \)	\( 3^{18} \cdot 7^{6} \cdot 23^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$90804$	$48$	$0$	$33.87713456$	$1$		$2$	$13049856$	$2.644527$	$165231457514151553/621021226401$	$0.98614$	$4.42942$	$[1, -1, 0, -5041521, -4341597408]$	\(y^2+xy=x^3-x^2-5041521x-4341597408\)	2.6.0.a.1, 84.12.0.?, 92.12.0.?, 188.12.0.?, 1932.24.0.?, $\ldots$	$[(8637896811730512/1302731, 699893801613024079242084/1302731)]$	$1$

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