Elliptic curve search results

Results (17 matches)

 

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
5610.bc2	5610bb3	5610.bc	5610bb	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)	\( 2^{2} \cdot 3^{4} \cdot 5^{4} \cdot 11^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.30	2Cs	$4488$	$192$	$1$	$1$	$1$		$2$	$24576$	$1.468594$	$870220733067747361/247623269602500$	$0.96701$	$4.78522$	$[1, 1, 1, -19890, -778053]$	\(y^2+xy+y=x^3+x^2-19890x-778053\)	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.c.1.2, 136.96.0.?, 264.96.0.?, $\ldots$	$[]$
16830.l2	16830t3	16830.l	16830t	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 17 \)	\( 2^{2} \cdot 3^{10} \cdot 5^{4} \cdot 11^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$4488$	$192$	$1$	$1.557101118$	$1$		$12$	$196608$	$2.017899$	$870220733067747361/247623269602500$	$0.96701$	$4.92237$	$[1, -1, 0, -179010, 20828416]$	\(y^2+xy=x^3-x^2-179010x+20828416\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 12.24.0-4.b.1.1, 24.48.0-8.c.1.1, $\ldots$	$[(122, 830)]$
28050.bg2	28050y4	28050.bg	28050y	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 \)	\( 2^{2} \cdot 3^{4} \cdot 5^{10} \cdot 11^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$22440$	$192$	$1$	$1$	$1$		$2$	$589824$	$2.273312$	$870220733067747361/247623269602500$	$0.96701$	$4.97612$	$[1, 0, 1, -497251, -96262102]$	\(y^2+xy+y=x^3-497251x-96262102\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 20.24.0-4.b.1.1, 40.48.0-8.c.1.2, $\ldots$	$[]$
44880.cu2	44880cy4	44880.cu	44880cy	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)	\( 2^{14} \cdot 3^{4} \cdot 5^{4} \cdot 11^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.23	2Cs	$4488$	$192$	$1$	$1$	$1$		$7$	$589824$	$2.161743$	$870220733067747361/247623269602500$	$0.96701$	$4.63279$	$[0, 1, 0, -318240, 49158900]$	\(y^2=x^3+x^2-318240x+49158900\)	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.c.1.9, 136.96.0.?, 264.96.0.?, $\ldots$	$[]$
61710.m2	61710o4	61710.m	61710o	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 17 \)	\( 2^{2} \cdot 3^{4} \cdot 5^{4} \cdot 11^{10} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$4488$	$192$	$1$	$2.576804270$	$1$		$8$	$2949120$	$2.667542$	$870220733067747361/247623269602500$	$0.96701$	$5.04931$	$[1, 1, 0, -2406692, 1023554844]$	\(y^2+xy=x^3+x^2-2406692x+1023554844\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 24.48.0-8.c.1.4, 44.24.0-4.b.1.1, $\ldots$	$[(-742, 49376)]$
84150.fo2	84150fu4	84150.fo	84150fu	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 \)	\( 2^{2} \cdot 3^{10} \cdot 5^{10} \cdot 11^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$22440$	$192$	$1$	$2.354027300$	$1$		$6$	$4718592$	$2.822620$	$870220733067747361/247623269602500$	$0.96701$	$5.07531$	$[1, -1, 1, -4475255, 2599076747]$	\(y^2+xy+y=x^3-x^2-4475255x+2599076747\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 60.24.0-4.b.1.1, 120.48.0.?, $\ldots$	$[(1863, 25996)]$
95370.dc2	95370db4	95370.dc	95370db	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17^{2} \)	\( 2^{2} \cdot 3^{4} \cdot 5^{4} \cdot 11^{4} \cdot 17^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.77	2Cs	$4488$	$192$	$1$	$1$	$4$	$2$	$2$	$7077888$	$2.885201$	$870220733067747361/247623269602500$	$0.96701$	$5.08540$	$[1, 0, 0, -5748216, -3782336004]$	\(y^2+xy=x^3-5748216x-3782336004\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.c.1.1, 68.24.0-4.b.1.1, 136.96.0.?, $\ldots$	$[]$
134640.be2	134640cd4	134640.be	134640cd	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 17 \)	\( 2^{14} \cdot 3^{10} \cdot 5^{4} \cdot 11^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$4488$	$192$	$1$	$6.645410601$	$1$		$5$	$4718592$	$2.711048$	$870220733067747361/247623269602500$	$0.96701$	$4.75997$	$[0, 0, 0, -2864163, -1330154462]$	\(y^2=x^3-2864163x-1330154462\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 12.24.0-4.b.1.3, 24.48.0-8.c.1.8, $\ldots$	$[(-849, 22126)]$
179520.v2	179520dx3	179520.v	179520dx	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)	\( 2^{20} \cdot 3^{4} \cdot 5^{4} \cdot 11^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.8	2Cs	$4488$	$192$	$1$	$2.829657160$	$1$		$7$	$4718592$	$2.508316$	$870220733067747361/247623269602500$	$0.96701$	$4.44569$	$[0, -1, 0, -1272961, 394544161]$	\(y^2=x^3-x^2-1272961x+394544161\)	2.6.0.a.1, 4.24.0-4.b.1.2, 8.48.0-8.c.1.5, 136.96.0.?, 264.96.0.?, $\ldots$	$[(-747, 30464)]$
179520.fi2	179520ga4	179520.fi	179520ga	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)	\( 2^{20} \cdot 3^{4} \cdot 5^{4} \cdot 11^{4} \cdot 17^{4} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.7	2Cs	$4488$	$192$	$1$	$3.231057520$	$1$		$23$	$4718592$	$2.508316$	$870220733067747361/247623269602500$	$0.96701$	$4.44569$	$[0, 1, 0, -1272961, -394544161]$	\(y^2=x^3+x^2-1272961x-394544161\)	2.6.0.a.1, 4.24.0-4.b.1.2, 8.48.0-8.c.1.10, 136.96.0.?, 264.96.0.?, $\ldots$	$[(-391, 6600), (-358, 3927)]$
185130.dp2	185130bf4	185130.dp	185130bf	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 17 \)	\( 2^{2} \cdot 3^{10} \cdot 5^{4} \cdot 11^{10} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.127	2Cs	$4488$	$192$	$1$	$7.948416180$	$1$		$4$	$23592960$	$3.216846$	$870220733067747361/247623269602500$	$0.96701$	$5.13542$	$[1, -1, 1, -21660233, -27657641019]$	\(y^2+xy+y=x^3-x^2-21660233x-27657641019\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.c.1.3, 132.24.0.?, 136.96.0.?, $\ldots$	$[(-1533, 44846)]$
224400.co2	224400fd3	224400.co	224400fd	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 \)	\( 2^{14} \cdot 3^{4} \cdot 5^{10} \cdot 11^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$22440$	$192$	$1$	$2.359248090$	$1$		$9$	$14155776$	$2.966461$	$870220733067747361/247623269602500$	$0.96701$	$4.81138$	$[0, -1, 0, -7956008, 6160774512]$	\(y^2=x^3-x^2-7956008x+6160774512\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 20.24.0-4.b.1.3, 40.48.0-8.c.1.9, $\ldots$	$[(-398, 96250)]$
274890.ew2	274890ew3	274890.ew	274890ew	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 17 \)	\( 2^{2} \cdot 3^{4} \cdot 5^{4} \cdot 7^{6} \cdot 11^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$31416$	$192$	$1$	$1$	$1$		$2$	$9437184$	$2.441547$	$870220733067747361/247623269602500$	$0.96701$	$4.23047$	$[1, 0, 0, -974611, 263948285]$	\(y^2+xy=x^3-974611x+263948285\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 28.24.0-4.b.1.1, 56.48.0-8.c.1.1, $\ldots$	$[]$
286110.co2	286110co3	286110.co	286110co	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 17^{2} \)	\( 2^{2} \cdot 3^{10} \cdot 5^{4} \cdot 11^{4} \cdot 17^{10} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$4488$	$192$	$1$	$6.307905697$	$1$		$4$	$56623104$	$3.434505$	$870220733067747361/247623269602500$	$0.96701$	$5.16538$	$[1, -1, 0, -51733944, 102123072108]$	\(y^2+xy=x^3-x^2-51733944x+102123072108\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 24.48.0-8.c.1.2, 88.48.0.?, $\ldots$	$[(14787, 1595799)]$
308550.jf2	308550jf3	308550.jf	308550jf	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{2} \cdot 3^{4} \cdot 5^{10} \cdot 11^{10} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$22440$	$192$	$1$	$8.035066857$	$1$		$2$	$70778880$	$3.472260$	$870220733067747361/247623269602500$	$0.96701$	$5.17036$	$[1, 0, 0, -60167313, 128064690117]$	\(y^2+xy=x^3-60167313x+128064690117\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 120.48.0.?, 136.48.0.?, $\ldots$	$[(864894/5, 782986437/5)]$
476850.br2	476850br4	476850.br	476850br	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17^{2} \)	\( 2^{2} \cdot 3^{4} \cdot 5^{10} \cdot 11^{4} \cdot 17^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$22440$	$192$	$1$	$1$	$1$		$2$	$169869312$	$3.689919$	$870220733067747361/247623269602500$	$0.96701$	$5.19798$	$[1, 1, 0, -143705400, -472792000500]$	\(y^2+xy=x^3+x^2-143705400x-472792000500\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 40.48.0-8.c.1.1, 136.48.0.?, $\ldots$	$[]$
493680.go2	493680go4	493680.go	493680go	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{4} \cdot 5^{4} \cdot 11^{10} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.22	2Cs	$4488$	$192$	$1$	$5.294062494$	$1$		$5$	$70778880$	$3.360687$	$870220733067747361/247623269602500$	$0.96701$	$4.88287$	$[0, 1, 0, -38507080, -65584524172]$	\(y^2=x^3+x^2-38507080x-65584524172\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.c.1, 24.48.0-8.c.1.7, 44.24.0-4.b.1.3, $\ldots$	$[(-4324, 141750)]$