Elliptic curve search results

Results (1-50 of 2086 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
234446.a1	234446a1	234446.a	234446a	$1$	$1$	\( 2 \cdot 117223 \)	\( 2^{2} \cdot 117223 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1.504344888$	$1$		$64$	$334976$	$-0.086976$	$54915331401/468892$	$[1, -1, 0, -79, 289]$	\(y^2+xy=x^3-x^2-79x+289\)
501029.a1	-	501029.a	-	$1$	$1$	\( 501029 \)	\( 501029 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.169423835$	$1$		$42$	$271872$	$-0.095006$	$41854210048/501029$	$[0, 1, 1, -72, 210]$	\(y^2+y=x^3+x^2-72x+210\)
545723.a1	-	545723.a	-	$1$	$1$	\( 545723 \)	\( -545723 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.306378474$	$1$		$56$	$514560$	$-0.217695$	$-37933056/545723$	$[0, 0, 1, -7, 36]$	\(y^2+y=x^3-7x+36\)
602461.a1	-	602461.a	-	$1$	$1$	\( 602461 \)	\( -602461 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$4.459211538$	$1$		$36$	$233664$	$0.048303$	$-911826451873/602461$	$[1, 0, 0, -202, 1089]$	\(y^2+xy=x^3-202x+1089\)
797611.a1	-	797611.a	-	$1$	$1$	\( 797611 \)	\( -797611 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$4.590880369$	$1$		$48$	$365712$	$-0.188469$	$-1404928/797611$	$[0, 1, 1, -2, 42]$	\(y^2+y=x^3+x^2-2x+42\)
812011.a1	-	812011.a	-	$1$	$1$	\( 812011 \)	\( -812011 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$4.031919540$	$1$		$44$	$322992$	$-0.145152$	$-3738308608/812011$	$[0, 1, 1, -32, 72]$	\(y^2+y=x^3+x^2-32x+72\)
887657.a1	-	887657.a	-	$1$	$1$	\( 887657 \)	\( 887657 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5.398224908$	$1$		$32$	$227936$	$-0.110150$	$13027640977/887657$	$[1, 0, 0, -49, 120]$	\(y^2+xy=x^3-49x+120\)
953243.a1	-	953243.a	-	$1$	$1$	\( 953243 \)	\( -953243 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.366212426$	$1$		$48$	$925664$	$-0.073058$	$-33261981696/953243$	$[0, 0, 1, -67, 216]$	\(y^2+y=x^3-67x+216\)
1000033.a1	-	1000033.a	-	$1$	$1$	\( 1000033 \)	\( -1000033 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5.148236317$	$1$		$36$	$333488$	$-0.145877$	$-1732323601/1000033$	$[1, 0, 0, -25, 66]$	\(y^2+xy=x^3-25x+66\)
1129211.a1	-	1129211.a	-	$1$	$1$	\( 1129211 \)	\( -1129211 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$4.312445190$	$1$		$44$	$687616$	$-0.146811$	$-758550528/1129211$	$[0, 0, 1, -19, 60]$	\(y^2+y=x^3-19x+60\)
1241437.a1	-	1241437.a	-	$1$	$1$	\( 1241437 \)	\( 1241437 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.320066768$	$1$		$24$	$309312$	$-0.121076$	$4878401536/1241437$	$[0, -1, 1, -35, 72]$	\(y^2+y=x^3-x^2-35x+72\)
1321589.a1	-	1321589.a	-	$1$	$1$	\( 1321589 \)	\( 1321589 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$7.871921069$	$1$		$24$	$269728$	$-0.071237$	$23100424192/1321589$	$[0, 1, 1, -59, 147]$	\(y^2+y=x^3+x^2-59x+147\)
1549501.a1	-	1549501.a	-	$1$	$1$	\( 1549501 \)	\( -1549501 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$7.300544541$	$1$		$36$	$399840$	$-0.129405$	$-192100033/1549501$	$[1, 0, 0, -12, 61]$	\(y^2+xy=x^3-12x+61\)
1736437.a1	-	1736437.a	-	$1$	$1$	\( 1736437 \)	\( 1736437 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5.455919233$	$1$		$36$	$896816$	$0.056076$	$455821889536/1736437$	$[0, -1, 1, -160, 832]$	\(y^2+y=x^3-x^2-160x+832\)
1740197.a1	-	1740197.a	-	$1$	$1$	\( 1740197 \)	\( 1740197 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$4.816457485$	$1$		$44$	$1483552$	$-0.112482$	$3086626816/1740197$	$[0, 1, 1, -30, 0]$	\(y^2+y=x^3+x^2-30x\)
1764029.a1	-	1764029.a	-	$1$	$1$	\( 1764029 \)	\( 1764029 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$7.377733813$	$1$		$36$	$360880$	$-0.103586$	$4354703137/1764029$	$[1, 0, 0, -34, 39]$	\(y^2+xy=x^3-34x+39\)
2184811.a1	-	2184811.a	-	$1$	$1$	\( 2184811 \)	\( -2184811 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.083562203$	$1$		$34$	$688576$	$-0.101398$	$425259008/2184811$	$[0, 1, 1, 16, 72]$	\(y^2+y=x^3+x^2+16x+72\)
2216309.a1	-	2216309.a	-	$1$	$1$	\( 2216309 \)	\( 2216309 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5.392257093$	$1$		$38$	$1350688$	$0.050913$	$318891962368/2216309$	$[0, 1, 1, -142, 602]$	\(y^2+y=x^3+x^2-142x+602\)
2609963.a1	-	2609963.a	-	$1$	$1$	\( 2609963 \)	\( -2609963 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.120830535$	$1$		$38$	$1204096$	$-0.070281$	$-3294646272/2609963$	$[0, 0, 1, -31, 102]$	\(y^2+y=x^3-31x+102\)
2614763.a1	-	2614763.a	-	$1$	$1$	\( 2614763 \)	\( -2614763 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$7.386759033$	$1$		$34$	$922752$	$-0.087767$	$-122023936/2614763$	$[0, -1, 1, -10, 82]$	\(y^2+y=x^3-x^2-10x+82\)
2697179.a1	-	2697179.a	-	$1$	$1$	\( 2697179 \)	\( -2697179 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.151905214$	$1$		$30$	$983152$	$-0.047748$	$-11000295424/2697179$	$[0, -1, 1, -46, 160]$	\(y^2+y=x^3-x^2-46x+160\)
3001421.a1	-	3001421.a	-	$1$	$1$	\( 3001421 \)	\( 3001421 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$11.34264301$	$1$		$20$	$694016$	$0.062928$	$312217698304/3001421$	$[0, 1, 1, -141, 594]$	\(y^2+y=x^3+x^2-141x+594\)
3254773.a1	-	3254773.a	-	$1$	$1$	\( 3254773 \)	\( -3254773 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.065065159$	$1$		$26$	$779648$	$-0.019567$	$-22737343537/3254773$	$[1, 0, 0, -59, 190]$	\(y^2+xy=x^3-59x+190\)
3261221.a1	-	3261221.a	-	$1$	$1$	\( 3261221 \)	\( -3261221 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10.44284528$	$1$		$38$	$1420080$	$-0.061051$	$5295319407/3261221$	$[1, -1, 1, 36, 12]$	\(y^2+xy+y=x^3-x^2+36x+12\)
3280363.a1	-	3280363.a	-	$1$	$1$	\( 3280363 \)	\( -3280363 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.262826529$	$1$		$34$	$1658880$	$-0.017436$	$-24288219136/3280363$	$[0, 1, 1, -60, 180]$	\(y^2+y=x^3+x^2-60x+180\)
3349097.a1	-	3349097.a	-	$1$	$1$	\( 3349097 \)	\( 3349097 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.669148031$	$1$		$30$	$1498816$	$0.326366$	$71333963490817/3349097$	$[1, 0, 0, -864, 9703]$	\(y^2+xy=x^3-864x+9703\)
3525883.a1	-	3525883.a	-	$1$	$1$	\( 3525883 \)	\( -3525883 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.476405941$	$1$		$38$	$2072448$	$-0.058100$	$-929714176/3525883$	$[0, 1, 1, -20, 90]$	\(y^2+y=x^3+x^2-20x+90\)
3643883.a1	-	3643883.a	-	$1$	$1$	\( 3643883 \)	\( -3643883 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.316606704$	$1$		$40$	$3223536$	$-0.039848$	$-5601816576/3643883$	$[0, 0, 1, -37, 126]$	\(y^2+y=x^3-37x+126\)
3651607.a1	-	3651607.a	-	$1$	$1$	\( 3651607 \)	\( 3651607 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$7.958379789$	$1$		$34$	$1359936$	$0.027713$	$96892315857/3651607$	$[1, -1, 1, -96, 372]$	\(y^2+xy+y=x^3-x^2-96x+372\)
3744737.a1	-	3744737.a	-	$1$	$1$	\( 3744737 \)	\( 3744737 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.606393285$	$1$		$36$	$1703040$	$0.048837$	$168288035761/3744737$	$[1, 0, 0, -115, 456]$	\(y^2+xy=x^3-115x+456\)
3806051.a1	-	3806051.a	-	$1$	$1$	\( 3806051 \)	\( -3806051 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$15.74008379$	$1$		$28$	$715872$	$-0.048277$	$6058428767/3806051$	$[1, 1, 1, 38, 42]$	\(y^2+xy+y=x^3+x^2+38x+42\)
4032949.a1	-	4032949.a	-	$1$	$1$	\( 4032949 \)	\( 4032949 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.930437577$	$1$		$34$	$2607040$	$0.004994$	$41854210048/4032949$	$[0, -1, 1, -72, 240]$	\(y^2+y=x^3-x^2-72x+240\)
4036069.c1	-	4036069.c	-	$1$	$1$	\( 4036069 \)	\( 4036069 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$15.80299929$	$1$		$28$	$8873664$	$0.904597$	$1051350717450682368/4036069$	$[0, 0, 1, -21184, 1186752]$	\(y^2+y=x^3-21184x+1186752\)
4077611.a1	-	4077611.a	-	$1$	$1$	\( 4077611 \)	\( -4077611 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.405311874$	$1$		$42$	$3371520$	$-0.047458$	$-758550528/4077611$	$[0, 0, 1, -19, 102]$	\(y^2+y=x^3-19x+102\)
4092701.a1	-	4092701.a	-	$1$	$1$	\( 4092701 \)	\( -4092701 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$9.472367748$	$1$		$30$	$1808448$	$0.259594$	$-17610498546913/4092701$	$[1, 1, 1, -542, 4632]$	\(y^2+xy+y=x^3+x^2-542x+4632\)
4225973.a1	-	4225973.a	-	$1$	$1$	\( 4225973 \)	\( 4225973 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$7.936599835$	$1$		$32$	$2346800$	$0.137666$	$1316532736000/4225973$	$[0, 1, 1, -228, 1248]$	\(y^2+y=x^3+x^2-228x+1248\)
4248019.a1	-	4248019.a	-	$1$	$1$	\( 4248019 \)	\( -4248019 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$26.14450159$	$1$		$20$	$773088$	$-0.048527$	$71991296/4248019$	$[0, 1, 1, 9, -96]$	\(y^2+y=x^3+x^2+9x-96\)
4258363.a1	-	4258363.a	-	$1$	$1$	\( 4258363 \)	\( -4258363 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.572756889$	$1$		$38$	$2268768$	$0.051661$	$-148540174336/4258363$	$[0, 1, 1, -110, 420]$	\(y^2+y=x^3+x^2-110x+420\)
4343629.a1	-	4343629.a	-	$1$	$1$	\( 4343629 \)	\( 4343629 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$13.17846994$	$1$		$20$	$1045312$	$0.068844$	$239251750912/4343629$	$[0, -1, 1, -129, 600]$	\(y^2+y=x^3-x^2-129x+600\)
4459157.a1	-	4459157.a	-	$1$	$1$	\( 4459157 \)	\( 4459157 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$11.47340939$	$1$		$26$	$1435360$	$0.000737$	$30371328000/4459157$	$[0, 0, 1, -65, 174]$	\(y^2+y=x^3-65x+174\)
4513931.a1	-	4513931.a	-	$1$	$1$	\( 4513931 \)	\( -4513931 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10.28230001$	$1$		$26$	$1100512$	$-0.035979$	$-1593413632/4513931$	$[0, -1, 1, -24, 120]$	\(y^2+y=x^3-x^2-24x+120\)
4573691.a1	-	4573691.a	-	$1$	$1$	\( 4573691 \)	\( -4573691 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.220042391$	$1$		$32$	$1928992$	$0.015846$	$-41854210048/4573691$	$[0, -1, 1, -72, 282]$	\(y^2+y=x^3-x^2-72x+282\)
4592017.a1	-	4592017.a	-	$1$	$1$	\( 4592017 \)	\( 4592017 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$7.817506761$	$1$		$34$	$3070544$	$-0.031995$	$8012006001/4592017$	$[1, -1, 1, -42, 0]$	\(y^2+xy+y=x^3-x^2-42x\)
4695371.a1	-	4695371.a	-	$1$	$1$	\( 4695371 \)	\( -4695371 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.048759322$	$1$		$44$	$4356544$	$0.055159$	$-143219847168/4695371$	$[0, 0, 1, -109, 450]$	\(y^2+y=x^3-109x+450\)
4732603.a1	-	4732603.a	-	$1$	$1$	\( 4732603 \)	\( -4732603 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.243641382$	$1$		$38$	$6784000$	$0.469587$	$-795464207036416/4732603$	$[0, 1, 1, -1930, 32000]$	\(y^2+y=x^3+x^2-1930x+32000\)
4839157.a1	-	4839157.a	-	$1$	$1$	\( 4839157 \)	\( 4839157 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$9.290413346$	$1$		$40$	$2934656$	$-0.000179$	$25102282752/4839157$	$[0, 0, 1, -61, -150]$	\(y^2+y=x^3-61x-150\)
4883953.a1	-	4883953.a	-	$1$	$1$	\( 4883953 \)	\( -4883953 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10.34670453$	$1$		$30$	$1881472$	$0.322300$	$-53297461115137/4883953$	$[1, 0, 0, -784, 8385]$	\(y^2+xy=x^3-784x+8385\)
4953023.a1	-	4953023.a	-	$1$	$1$	\( 4953023 \)	\( -4953023 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$12.34399849$	$1$		$24$	$1373056$	$0.035743$	$-72043225281/4953023$	$[1, -1, 1, -87, 350]$	\(y^2+xy+y=x^3-x^2-87x+350\)
5031193.a1	-	5031193.a	-	$1$	$1$	\( 5031193 \)	\( -5031193 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.187677878$	$1$		$34$	$1797840$	$0.001955$	$-18420660721/5031193$	$[1, 0, 0, -55, 186]$	\(y^2+xy=x^3-55x+186\)
5097403.a1	-	5097403.a	-	$1$	$1$	\( 5097403 \)	\( -5097403 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.041967274$	$1$		$40$	$8643232$	$0.214891$	$-6084387721216/5097403$	$[0, 1, 1, -380, 2730]$	\(y^2+y=x^3+x^2-380x+2730\)