Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (1-50 of 759667 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
500393.a1	-	500393.a	-	$1$	$1$	\( 500393 \)	\( 500393 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5.708062262$	$1$		$4$	$35736$	$-0.214654$	$955671625/500393$	$[1, 0, 1, -21, -13]$	\(y^2+xy+y=x^3-21x-13\)
500719.a1	-	500719.a	-	$1$	$1$	\( 500719 \)	\( 500719 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$99450$	$0.079314$	$1944232280641/500719$	$[1, 1, 1, -260, -1722]$	\(y^2+xy+y=x^3+x^2-260x-1722\)
500921.a1	-	500921.a	-	$1$	$1$	\( 500921 \)	\( 500921 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$4.156797531$	$1$		$0$	$50640$	$-0.205827$	$1378749897/500921$	$[1, -1, 0, -23, 32]$	\(y^2+xy=x^3-x^2-23x+32\)
500921.b1	-	500921.b	-	$1$	$1$	\( 500921 \)	\( 500921 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$9.285837453$	$1$		$0$	$55576$	$-0.101954$	$35062107417/500921$	$[1, -1, 0, -68, -197]$	\(y^2+xy=x^3-x^2-68x-197\)
501029.a1	-	501029.a	-	$1$	$1$	\( 501029 \)	\( 501029 \)	$4$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.169423835$	$1$		$42$	$271872$	$-0.095006$	$41854210048/501029$	$[0, 1, 1, -72, 210]$	\(y^2+y=x^3+x^2-72x+210\)
501121.a1	-	501121.a	-	$1$	$1$	\( 501121 \)	\( 501121 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.822916517$	$1$		$6$	$102788$	$-0.169841$	$5026574097/501121$	$[1, -1, 1, -36, -66]$	\(y^2+xy+y=x^3-x^2-36x-66\)
501139.a1	-	501139.a	-	$1$	$1$	\( 501139 \)	\( 501139 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5.482767682$	$1$		$0$	$157954$	$-0.018553$	$252555814161/501139$	$[1, -1, 1, -132, -548]$	\(y^2+xy+y=x^3-x^2-132x-548\)
501139.b1	-	501139.b	-	$1$	$1$	\( 501139 \)	\( -501139 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$4$	$2$	$0$	$470488$	$0.655404$	$-40125329153118208/501139$	$[0, -1, 1, -7132, 234221]$	\(y^2+y=x^3-x^2-7132x+234221\)
501317.a1	-	501317.a	-	$1$	$1$	\( 501317 \)	\( 501317 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$34690$	$-0.136410$	$13824000000/501317$	$[0, 0, 1, -50, -132]$	\(y^2+y=x^3-50x-132\)
501341.a1	-	501341.a	-	$1$	$1$	\( 501341 \)	\( -501341 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.792395909$	$1$		$0$	$38242$	$-0.223833$	$109902239/501341$	$[1, 0, 0, 10, -31]$	\(y^2+xy=x^3+10x-31\)
501367.a1	-	501367.a	-	$1$	$1$	\( 501367 \)	\( -501367 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.254293117$	$1$		$0$	$56132$	$-0.222032$	$-95443993/501367$	$[1, 1, 0, -9, 32]$	\(y^2+xy=x^3+x^2-9x+32\)
501451.a1	-	501451.a	-	$1$	$1$	\( 501451 \)	\( -501451 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$58968$	$-0.218221$	$642735647/501451$	$[1, 1, 1, 18, -10]$	\(y^2+xy+y=x^3+x^2+18x-10\)
501563.a1	-	501563.a	-	$1$	$1$	\( 501563 \)	\( -501563 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.252577989$	$1$		$4$	$65852$	$-0.226033$	$20123648/501563$	$[0, 1, 1, 6, -32]$	\(y^2+y=x^3+x^2+6x-32\)
502237.a1	-	502237.a	-	$1$	$1$	\( 502237 \)	\( 502237 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$4.391473878$	$1$		$4$	$39360$	$-0.187938$	$2703045457/502237$	$[1, 0, 0, -29, -52]$	\(y^2+xy=x^3-29x-52\)
502237.b1	-	502237.b	-	$1$	$1$	\( 502237 \)	\( 502237 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.505377253$	$1$		$0$	$139586$	$-0.126093$	$18399744000/502237$	$[0, 0, 1, -55, 153]$	\(y^2+y=x^3-55x+153\)
502237.c1	-	502237.c	-	$1$	$1$	\( 502237 \)	\( 502237 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$73438$	$-0.202041$	$1593413632/502237$	$[0, -1, 1, -24, 39]$	\(y^2+y=x^3-x^2-24x+39\)
502507.a1	-	502507.a	-	$1$	$1$	\( 502507 \)	\( -502507 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2.767574032$	$1$		$0$	$175664$	$-0.118435$	$-21952000000/502507$	$[0, -1, 1, -58, 194]$	\(y^2+y=x^3-x^2-58x+194\)
502543.a1	-	502543.a	-	$1$	$1$	\( 502543 \)	\( -502543 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$4.048298968$	$1$		$2$	$38912$	$-0.212060$	$-426957777/502543$	$[1, -1, 1, -16, -38]$	\(y^2+xy+y=x^3-x^2-16x-38\)
502543.b1	-	502543.b	-	$1$	$1$	\( 502543 \)	\( -502543 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2.987990163$	$1$		$2$	$70872$	$-0.169654$	$-4354703137/502543$	$[1, 1, 1, -34, -98]$	\(y^2+xy+y=x^3+x^2-34x-98\)
502819.a1	-	502819.a	-	$1$	$1$	\( 502819 \)	\( -502819 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6.093750191$	$1$		$0$	$84090$	$-0.226544$	$5451776/502819$	$[0, 1, 1, 4, -33]$	\(y^2+y=x^3+x^2+4x-33\)
502829.a1	-	502829.a	-	$1$	$1$	\( 502829 \)	\( 502829 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2.499447655$	$1$		$2$	$40036$	$-0.179488$	$3623878656/502829$	$[0, 0, 1, -32, -61]$	\(y^2+y=x^3-32x-61\)
503621.a1	-	503621.a	-	$1$	$1$	\( 503621 \)	\( -503621 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$15.33182773$	$1$		$0$	$96750$	$-0.222951$	$139798359/503621$	$[1, -1, 0, 11, -34]$	\(y^2+xy=x^3-x^2+11x-34\)
503803.a1	-	503803.a	-	$1$	$1$	\( 503803 \)	\( -503803 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.246145804$	$1$		$6$	$51292$	$-0.217067$	$758550528/503803$	$[0, 0, 1, 19, 12]$	\(y^2+y=x^3+19x+12\)
503857.a1	-	503857.a	-	$1$	$1$	\( 503857 \)	\( -503857 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$4$	$2$	$0$	$40512$	$-0.226330$	$6128487/503857$	$[1, -1, 0, 4, -35]$	\(y^2+xy=x^3-x^2+4x-35\)
503963.a1	-	503963.a	-	$1$	$1$	\( 503963 \)	\( -503963 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$126428$	$-0.018213$	$-252555814161/503963$	$[1, -1, 1, -132, -550]$	\(y^2+xy+y=x^3-x^2-132x-550\)
504149.a1	-	504149.a	-	$1$	$1$	\( 504149 \)	\( -504149 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2.095780300$	$1$		$2$	$40534$	$-0.217029$	$756058031/504149$	$[1, 0, 0, 19, 14]$	\(y^2+xy=x^3+19x+14\)
504197.a1	-	504197.a	-	$1$	$1$	\( 504197 \)	\( 504197 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1.841983747$	$1$		$2$	$53998$	$-0.215959$	$884736000/504197$	$[0, 0, 1, -20, 4]$	\(y^2+y=x^3-20x+4\)
504299.a1	-	504299.a	-	$1$	$1$	\( 504299 \)	\( -504299 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$93911$	$-0.225878$	$-8998912/504299$	$[0, 1, 1, -4, -36]$	\(y^2+y=x^3+x^2-4x-36\)
504323.a1	-	504323.a	-	$1$	$1$	\( 504323 \)	\( -504323 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$4.578621953$	$1$		$0$	$45192$	$-0.226744$	$512000/504323$	$[0, -1, 1, 2, -35]$	\(y^2+y=x^3-x^2+2x-35\)
504521.a1	-	504521.a	-	$1$	$1$	\( 504521 \)	\( 504521 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$242216$	$0.453624$	$1545165254811529/504521$	$[1, 0, 1, -2409, -45697]$	\(y^2+xy+y=x^3-2409x-45697\)
504521.b1	-	504521.b	-	$1$	$1$	\( 504521 \)	\( -504521 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8.301270702$	$1$		$4$	$99904$	$-0.225749$	$-10218313/504521$	$[1, 0, 1, -5, -35]$	\(y^2+xy+y=x^3-5x-35\)
505033.a1	-	505033.a	-	$1$	$1$	\( 505033 \)	\( -505033 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2.419287806$	$1$		$2$	$67018$	$-0.226284$	$-3048625/505033$	$[1, 0, 0, -3, 34]$	\(y^2+xy=x^3-3x+34\)
505061.a1	-	505061.a	-	$1$	$1$	\( 505061 \)	\( 505061 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5.583878817$	$1$		$14$	$82896$	$0.105460$	$3231289442304/505061$	$[0, 0, 1, -308, 2080]$	\(y^2+y=x^3-308x+2080\)
505061.b1	-	505061.b	-	$1$	$1$	\( 505061 \)	\( -505061 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.195573343$	$1$		$4$	$113076$	$0.067280$	$-1519685060473/505061$	$[1, 0, 1, -240, 1407]$	\(y^2+xy+y=x^3-240x+1407\)
505111.a1	-	505111.a	-	$1$	$1$	\( 505111 \)	\( -505111 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$110532$	$-0.064877$	$-86175179713/505111$	$[1, 1, 1, -92, -380]$	\(y^2+xy+y=x^3+x^2-92x-380\)
505139.a1	-	505139.a	-	$1$	$1$	\( 505139 \)	\( -505139 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$63.45393117$	$1$		$0$	$248574$	$0.509319$	$-3853942412898304/505139$	$[0, 1, 1, -3266, -72941]$	\(y^2+y=x^3+x^2-3266x-72941\)
505187.a1	-	505187.a	-	$1$	$1$	\( 505187 \)	\( -505187 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$36.69619193$	$1$		$0$	$143862$	$-0.204832$	$-758550528/505187$	$[0, 0, 1, -19, -47]$	\(y^2+y=x^3-19x-47\)
505283.a1	-	505283.a	-	$1$	$1$	\( 505283 \)	\( -505283 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$216238$	$0.593425$	$-14965684732064737/505283$	$[1, 1, 1, -5134, -143730]$	\(y^2+xy+y=x^3+x^2-5134x-143730\)
505663.a1	-	505663.a	-	$1$	$1$	\( 505663 \)	\( -505663 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5.890557645$	$1$		$2$	$57504$	$-0.218320$	$541343375/505663$	$[1, 1, 1, 17, 28]$	\(y^2+xy+y=x^3+x^2+17x+28\)
505691.a1	-	505691.a	-	$1$	$1$	\( 505691 \)	\( -505691 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.656533502$	$1$		$14$	$133008$	$0.121001$	$-4359504941056/505691$	$[0, -1, 1, -340, 2530]$	\(y^2+y=x^3-x^2-340x+2530\)
505691.b1	-	505691.b	-	$1$	$1$	\( 505691 \)	\( -505691 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$11.55256907$	$1$		$4$	$82112$	$0.027104$	$-666940371553/505691$	$[1, 0, 0, -182, -961]$	\(y^2+xy=x^3-182x-961\)
505709.a1	-	505709.a	-	$1$	$1$	\( 505709 \)	\( 505709 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$425398$	$0.618357$	$22258232254222336/505709$	$[0, -1, 1, -5860, 174629]$	\(y^2+y=x^3-x^2-5860x+174629\)
505763.a1	-	505763.a	-	$1$	$1$	\( 505763 \)	\( -505763 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$125475$	$0.376911$	$-427434241687552/505763$	$[0, -1, 1, -1569, -23406]$	\(y^2+y=x^3-x^2-1569x-23406\)
505763.b1	-	505763.b	-	$1$	$1$	\( 505763 \)	\( -505763 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$44209$	$-0.204022$	$-799178752/505763$	$[0, 1, 1, -19, -54]$	\(y^2+y=x^3+x^2-19x-54\)
505819.a1	-	505819.a	-	$1$	$1$	\( 505819 \)	\( -505819 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$36003$	$-0.219025$	$452984832/505819$	$[0, 0, 1, 16, -24]$	\(y^2+y=x^3+16x-24\)
506251.a1	-	506251.a	-	$1$	$1$	\( 506251 \)	\( -506251 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3.201803163$	$1$		$6$	$69600$	$-0.226352$	$-884736/506251$	$[0, 0, 1, -2, 34]$	\(y^2+y=x^3-2x+34\)
506251.b1	-	506251.b	-	$1$	$1$	\( 506251 \)	\( -506251 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$63947$	$-0.221320$	$224755712/506251$	$[0, -1, 1, 13, 25]$	\(y^2+y=x^3-x^2+13x+25\)
506339.a1	-	506339.a	-	$1$	$1$	\( 506339 \)	\( 506339 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$4$	$2$	$0$	$213936$	$0.466834$	$1919244689134417/506339$	$[1, 1, 1, -2589, -51784]$	\(y^2+xy+y=x^3+x^2-2589x-51784\)
506459.a1	-	506459.a	-	$1$	$1$	\( 506459 \)	\( -506459 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$79407$	$0.025026$	$-637832691712/506459$	$[0, 1, 1, -179, 865]$	\(y^2+y=x^3+x^2-179x+865\)
506573.a1	-	506573.a	-	$1$	$1$	\( 506573 \)	\( -506573 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$5.214214958$	$1$		$0$	$44536$	$-0.216265$	$817400375/506573$	$[1, 1, 0, 20, 17]$	\(y^2+xy=x^3+x^2+20x+17\)

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