Elliptic curve search results

Results (29 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
1122.g2	1122g1	1122.g	1122g	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 17 \)	\( 2^{26} \cdot 3^{13} \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$16224$	$2.127087$	$7722211175253055152433/340131399900069888$	$1.02892$	$7.17633$	$[1, 1, 1, -411787, -97932871]$	\(y^2+xy+y=x^3+x^2-411787x-97932871\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
3366.b2	3366b1	3366.b	3366b	$2$	$2$	\( 2 \cdot 3^{2} \cdot 11 \cdot 17 \)	\( 2^{26} \cdot 3^{19} \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$129792$	$2.676395$	$7722211175253055152433/340131399900069888$	$1.02892$	$7.01720$	$[1, -1, 0, -3706083, 2640481429]$	\(y^2+xy=x^3-x^2-3706083x+2640481429\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
8976.bb2	8976bb1	8976.bb	8976bb	$2$	$2$	\( 2^{4} \cdot 3 \cdot 11 \cdot 17 \)	\( 2^{38} \cdot 3^{13} \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$389376$	$2.820236$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.45069$	$[0, 1, 0, -6588592, 6254526548]$	\(y^2=x^3+x^2-6588592x+6254526548\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
12342.e2	12342b1	12342.e	12342b	$2$	$2$	\( 2 \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{13} \cdot 11^{7} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$4$	$2$	$1$	$1946880$	$3.326035$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.87691$	$[1, 1, 0, -49826229, 130099519917]$	\(y^2+xy=x^3+x^2-49826229x+130099519917\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
19074.bc2	19074bb1	19074.bc	19074bb	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 17^{2} \)	\( 2^{26} \cdot 3^{13} \cdot 11 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.573506867$	$1$		$7$	$4672512$	$3.543694$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.83818$	$[1, 0, 0, -119006449, -480311149207]$	\(y^2+xy=x^3-119006449x-480311149207\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-6742, 128219)]$
26928.s2	26928bo1	26928.s	26928bo	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 11 \cdot 17 \)	\( 2^{38} \cdot 3^{19} \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$9$	$3$	$1$	$3115008$	$3.369541$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.40215$	$[0, 0, 0, -59297331, -168931514126]$	\(y^2=x^3-59297331x-168931514126\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
28050.bp2	28050bg1	28050.bp	28050bg	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 \)	\( 2^{26} \cdot 3^{13} \cdot 5^{6} \cdot 11 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.370524676$	$1$		$7$	$2076672$	$2.931805$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.86375$	$[1, 0, 1, -10294676, -12221019502]$	\(y^2+xy+y=x^3-10294676x-12221019502\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-2118, 10171)]$
35904.j2	35904cd1	35904.j	35904cd	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11 \cdot 17 \)	\( 2^{44} \cdot 3^{13} \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$3115008$	$3.166809$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.99460$	$[0, -1, 0, -26354369, 50062566753]$	\(y^2=x^3-x^2-26354369x+50062566753\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
35904.bz2	35904bf1	35904.bz	35904bf	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11 \cdot 17 \)	\( 2^{44} \cdot 3^{13} \cdot 11 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.801607507$	$1$		$3$	$3115008$	$3.166809$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.99460$	$[0, 1, 0, -26354369, -50062566753]$	\(y^2=x^3+x^2-26354369x-50062566753\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-2579, 27540)]$
37026.ba2	37026bk1	37026.ba	37026bk	$2$	$2$	\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{19} \cdot 11^{7} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.371727774$	$1$		$3$	$15575040$	$3.875340$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.78533$	$[1, -1, 1, -448436066, -3513135473823]$	\(y^2+xy+y=x^3-x^2-448436066x-3513135473823\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-11791, 373311)]$
54978.bx2	54978ca1	54978.bx	54978ca	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 \)	\( 2^{26} \cdot 3^{13} \cdot 7^{6} \cdot 11 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.256420853$	$1$		$15$	$5840640$	$3.100044$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.68718$	$[1, 0, 0, -20177564, 33530442000]$	\(y^2+xy=x^3-20177564x+33530442000\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(1912, 43108)]$
57222.z2	57222t1	57222.z	57222t	$2$	$2$	\( 2 \cdot 3^{2} \cdot 11 \cdot 17^{2} \)	\( 2^{26} \cdot 3^{19} \cdot 11 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$37.50994576$	$1$		$1$	$37380096$	$4.093002$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.75412$	$[1, -1, 0, -1071058041, 12968401028589]$	\(y^2+xy=x^3-x^2-1071058041x+12968401028589\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(685798721814952825/7801703, 722298539087366089563876316/7801703)]$
84150.gc2	84150ff1	84150.gc	84150ff	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 \)	\( 2^{26} \cdot 3^{19} \cdot 5^{6} \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$16613376$	$3.481113$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.87695$	$[1, -1, 1, -92652080, 329967526547]$	\(y^2+xy+y=x^3-x^2-92652080x+329967526547\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
98736.dc2	98736da1	98736.dc	98736da	$2$	$2$	\( 2^{4} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{38} \cdot 3^{13} \cdot 11^{7} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$46725120$	$4.019180$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.35672$	$[0, 1, 0, -797219672, -8327963714028]$	\(y^2=x^3+x^2-797219672x-8327963714028\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
107712.ds2	107712by1	107712.ds	107712by	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 \)	\( 2^{44} \cdot 3^{19} \cdot 11 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$29.28384635$	$1$		$1$	$24920064$	$3.716114$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.99512$	$[0, 0, 0, -237189324, 1351452113008]$	\(y^2=x^3-237189324x+1351452113008\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-27371571787651/55379, 282025507456921500981/55379)]$
107712.dy2	107712dk1	107712.dy	107712dk	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 \)	\( 2^{44} \cdot 3^{19} \cdot 11 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$26.61720397$	$1$		$1$	$24920064$	$3.716114$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.99512$	$[0, 0, 0, -237189324, -1351452113008]$	\(y^2=x^3-237189324x-1351452113008\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-39975606365579/66469, 68185409876748715023/66469)]$
152592.k2	152592bp1	152592.k	152592bp	$2$	$2$	\( 2^{4} \cdot 3 \cdot 11 \cdot 17^{2} \)	\( 2^{38} \cdot 3^{13} \cdot 11 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$32.95039195$	$1$		$1$	$112140288$	$4.236839$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.34370$	$[0, -1, 0, -1904103184, 30739913549248]$	\(y^2=x^3-x^2-1904103184x+30739913549248\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(16327474552183329/743585, 210196584421177276726508/743585)]$
164934.bd2	164934do1	164934.bd	164934do	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \cdot 17 \)	\( 2^{26} \cdot 3^{19} \cdot 7^{6} \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$46725120$	$3.649349$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.71579$	$[1, -1, 0, -181598076, -905321934000]$	\(y^2+xy=x^3-x^2-181598076x-905321934000\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
189618.b2	189618bj1	189618.b	189618bj	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{13} \cdot 11 \cdot 13^{6} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$9$	$3$	$1$	$35043840$	$3.409561$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.41342$	$[1, 1, 0, -69592006, -214810557164]$	\(y^2+xy=x^3+x^2-69592006x-214810557164\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
209814.bi2	209814bs1	209814.bi	209814bs	$2$	$2$	\( 2 \cdot 3 \cdot 11^{2} \cdot 17^{2} \)	\( 2^{26} \cdot 3^{13} \cdot 11^{7} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$3.362216487$	$1$		$3$	$560701440$	$4.742645$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.67416$	$[1, 0, 1, -14399780332, 639279739814186]$	\(y^2+xy+y=x^3-14399780332x+639279739814186\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(47377, 7938935)]$
224400.bf2	224400et1	224400.bf	224400et	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 \)	\( 2^{38} \cdot 3^{13} \cdot 5^{6} \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$49840128$	$3.624954$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.54920$	$[0, -1, 0, -164714808, 782145248112]$	\(y^2=x^3-x^2-164714808x+782145248112\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
296208.ba2	296208ba1	296208.ba	296208ba	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{38} \cdot 3^{19} \cdot 11^{7} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$9.117539590$	$1$		$1$	$373800960$	$4.568489$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.32561$	$[0, 0, 0, -7174977051, 224847845301706]$	\(y^2=x^3-7174977051x+224847845301706\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-330583/2, 127331325/2)]$
308550.ik2	308550ik1	308550.ik	308550ik	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{13} \cdot 5^{6} \cdot 11^{7} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.291463109$	$1$		$15$	$249200640$	$4.130753$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.88960$	$[1, 0, 0, -1245655738, 16264931301092]$	\(y^2+xy=x^3-1245655738x+16264931301092\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(12308, 1666550)]$
394944.u2	394944u1	394944.u	394944u	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{44} \cdot 3^{13} \cdot 11^{7} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$23.59133107$	$1$		$1$	$373800960$	$4.365753$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.99561$	$[0, -1, 0, -3188878689, -66620520833535]$	\(y^2=x^3-x^2-3188878689x-66620520833535\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(1291114863592/2243, 1428129879326590407/2243)]$
394944.ft2	394944ft1	394944.ft	394944ft	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{44} \cdot 3^{13} \cdot 11^{7} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$6.609776994$	$1$		$3$	$373800960$	$4.365753$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.99561$	$[0, 1, 0, -3188878689, 66620520833535]$	\(y^2=x^3+x^2-3188878689x+66620520833535\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-52878, 9348453)]$
405042.br2	405042br1	405042.br	405042br	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 17 \cdot 19^{2} \)	\( 2^{26} \cdot 3^{13} \cdot 11 \cdot 17^{2} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$3.859067100$	$1$		$5$	$115644672$	$3.599308$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.27156$	$[1, 0, 1, -148655115, 670532320054]$	\(y^2+xy+y=x^3-148655115x+670532320054\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-49, 823320)]$
439824.o2	439824o1	439824.o	439824o	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 \)	\( 2^{38} \cdot 3^{13} \cdot 7^{6} \cdot 11 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$30.44742051$	$1$		$1$	$140175360$	$3.793190$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.41719$	$[0, -1, 0, -322841024, -2145948288000]$	\(y^2=x^3-x^2-322841024x-2145948288000\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(820814084888866/118315, 22252840641685304125286/118315)]$
457776.em2	457776em1	457776.em	457776em	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 11 \cdot 17^{2} \)	\( 2^{38} \cdot 3^{19} \cdot 11 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$46.39259883$	$1$		$1$	$897122304$	$4.786148$	$7722211175253055152433/340131399900069888$	$1.02892$	$6.31473$	$[0, 0, 0, -17136928659, -829960528901038]$	\(y^2=x^3-17136928659x-829960528901038\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(503089916114174384981839/296167847, 356742056314464365949360049062321606/296167847)]$
476850.l2	476850l1	476850.l	476850l	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17^{2} \)	\( 2^{26} \cdot 3^{13} \cdot 5^{6} \cdot 11 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4488$	$12$	$0$	$25.26378735$	$1$		$1$	$598081536$	$4.348412$	$7722211175253055152433/340131399900069888$	$1.02892$	$5.89327$	$[1, 1, 0, -2975161225, -60038893650875]$	\(y^2+xy=x^3+x^2-2975161225x-60038893650875\)	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-464898179655/3904, 91782743316825485/3904)]$

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