Elliptic curve search results

Results (26 matches)

  Download displayed columns for results to

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
1290.f1	1290h1	1290.f	1290h	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{9} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1720$	$2$	$0$	$1$	$1$		$0$	$1068480$	$3.994469$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$9.94135$	$[1, 0, 1, 120229952, -3351306510322]$	\(y^2+xy+y=x^3+120229952x-3351306510322\)	1720.2.0.?	$[ ]$
3870.m1	3870u1	3870.m	3870u	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{53} \cdot 3^{14} \cdot 5^{9} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$1$		$0$	$8547840$	$4.543777$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$9.41720$	$[1, -1, 1, 1082069572, 90485275778687]$	\(y^2+xy+y=x^3-x^2+1082069572x+90485275778687\)	1720.2.0.?	$[ ]$
6450.be1	6450x1	6450.be	6450x	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{15} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$1$		$0$	$25643520$	$4.799187$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$9.21820$	$[1, 1, 1, 3005748812, -418913313790219]$	\(y^2+xy+y=x^3+x^2+3005748812x-418913313790219\)	1720.2.0.?	$[ ]$
10320.r1	10320w1	10320.r	10320w	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{65} \cdot 3^{8} \cdot 5^{9} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$7.131233936$	$1$		$2$	$25643520$	$4.687614$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$8.60453$	$[0, -1, 0, 1923679240, 214483616660592]$	\(y^2=x^3-x^2+1923679240x+214483616660592\)	1720.2.0.?	$[(-15646, 13437090)]$
19350.bh1	19350q1	19350.bh	19350q	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{14} \cdot 5^{15} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$49$	$7$	$0$	$205148160$	$5.348495$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$8.86000$	$[1, -1, 0, 27051739308, 11310686524075216]$	\(y^2+xy=x^3-x^2+27051739308x+11310686524075216\)	1720.2.0.?	$[ ]$
30960.w1	30960bh1	30960.w	30960bh	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{65} \cdot 3^{14} \cdot 5^{9} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$120.4793189$	$1$		$0$	$205148160$	$5.236923$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$8.32781$	$[0, 0, 0, 17313113157, -5791074962949142]$	\(y^2=x^3+17313113157x-5791074962949142\)	1720.2.0.?	$[(2181027042449684377510415706448124200613444733588651698029/49398215478043577533923617, 102545506629820987078051101903766507214900284965584425641630312101229007919967583076352/49398215478043577533923617)]$
41280.d1	41280f1	41280.d	41280f	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{71} \cdot 3^{8} \cdot 5^{9} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$95.49504863$	$1$		$0$	$205148160$	$5.034187$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.87349$	$[0, -1, 0, 7694716959, -1715876628001695]$	\(y^2=x^3-x^2+7694716959x-1715876628001695\)	1720.2.0.?	$[(4893127057341171647728986425537640768294591/2458081462019461799, 10869708134086013600556638905758325109194082161556637800832301392/2458081462019461799)]$
41280.cn1	41280dc1	41280.cn	41280dc	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{71} \cdot 3^{8} \cdot 5^{9} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$25$	$5$	$0$	$205148160$	$5.034187$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.87349$	$[0, 1, 0, 7694716959, 1715876628001695]$	\(y^2=x^3+x^2+7694716959x+1715876628001695\)	1720.2.0.?	$[ ]$
51600.cd1	51600dl1	51600.cd	51600dl	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{65} \cdot 3^{8} \cdot 5^{15} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$1$		$0$	$615444480$	$5.492332$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$8.21823$	$[0, 1, 0, 48091980992, 26810548266535988]$	\(y^2=x^3+x^2+48091980992x+26810548266535988\)	1720.2.0.?	$[ ]$
55470.v1	55470u1	55470.v	55470u	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 43^{2} \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{9} \cdot 43^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$7.995546653$	$1$		$0$	$1974551040$	$5.875069$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$8.58427$	$[1, 1, 1, 222305182134, 266453215936879959]$	\(y^2+xy+y=x^3+x^2+222305182134x+266453215936879959\)	1720.2.0.?	$[(86299249/13, 1573216498391/13)]$
63210.g1	63210e1	63210.g	63210e	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{9} \cdot 7^{6} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$143.2746333$	$1$		$0$	$352598400$	$4.967422$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.49753$	$[1, 1, 0, 5891267672, 1149504024308032]$	\(y^2+xy=x^3+x^2+5891267672x+1149504024308032\)	1720.2.0.?	$[(-128802546989073700589905461745776761256855103392015072624273461/95437170718382067389646624434, 28352296638983283633352805874827383779923137244430427226482715859949210610498712112761797373245/95437170718382067389646624434)]$
123840.ec1	123840ct1	123840.ec	123840ct	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{71} \cdot 3^{14} \cdot 5^{9} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$14.77489290$	$1$		$0$	$1641185280$	$5.583496$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.69798$	$[0, 0, 0, 69252452628, 46328599703593136]$	\(y^2=x^3+69252452628x+46328599703593136\)	1720.2.0.?	$[(79087497430/1021, 242750140673163264/1021)]$
123840.gb1	123840gm1	123840.gb	123840gm	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{71} \cdot 3^{14} \cdot 5^{9} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$28.52974936$	$1$		$0$	$1641185280$	$5.583496$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.69798$	$[0, 0, 0, 69252452628, -46328599703593136]$	\(y^2=x^3+69252452628x-46328599703593136\)	1720.2.0.?	$[(4311678981887534362/3088497, 8192408167920965192253440000/3088497)]$
154800.bd1	154800bq1	154800.bd	154800bq	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 43 \)	\( - 2^{65} \cdot 3^{14} \cdot 5^{15} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$25$	$5$	$0$	$4923555840$	$6.041641$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$8.01430$	$[0, 0, 0, 432827828925, -723884370368642750]$	\(y^2=x^3+432827828925x-723884370368642750\)	1720.2.0.?	$[ ]$
156090.by1	156090i1	156090.by	156090i	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{9} \cdot 11^{6} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$0.247170855$	$1$		$6$	$1367654400$	$5.193420$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.15754$	$[1, 0, 0, 14547824250, 4460603513062500]$	\(y^2+xy=x^3+14547824250x+4460603513062500\)	1720.2.0.?	$[(597420, 475492650)]$
166410.bh1	166410bu1	166410.bh	166410bu	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 43^{2} \)	\( - 2^{53} \cdot 3^{14} \cdot 5^{9} \cdot 43^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$9$	$3$	$0$	$15796408320$	$6.424377$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$8.34811$	$[1, -1, 0, 2000746639206, -7194234829549119692]$	\(y^2+xy=x^3-x^2+2000746639206x-7194234829549119692\)	1720.2.0.?	$[ ]$
189630.ea1	189630e1	189630.ea	189630e	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{14} \cdot 5^{9} \cdot 7^{6} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$1$		$0$	$2820787200$	$5.516731$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.36216$	$[1, -1, 1, 53021409043, -31036555634907819]$	\(y^2+xy+y=x^3-x^2+53021409043x-31036555634907819\)	1720.2.0.?	$[ ]$
206400.w1	206400dx1	206400.w	206400dx	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{71} \cdot 3^{8} \cdot 5^{15} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$16$	$2$	$0$	$4923555840$	$5.838905$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.62710$	$[0, -1, 0, 192367923967, 214484193764363937]$	\(y^2=x^3-x^2+192367923967x+214484193764363937\)	1720.2.0.?	$[ ]$
206400.js1	206400hs1	206400.js	206400hs	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{71} \cdot 3^{8} \cdot 5^{15} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$44.94276774$	$1$		$0$	$4923555840$	$5.838905$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.62710$	$[0, 1, 0, 192367923967, -214484193764363937]$	\(y^2=x^3+x^2+192367923967x-214484193764363937\)	1720.2.0.?	$[(17483911504416804268867387/5887351513, 21306297404763146228123305110405120000/5887351513)]$
218010.cd1	218010r1	218010.cd	218010r	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{9} \cdot 13^{6} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$1$		$0$	$2397669120$	$5.276947$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.04454$	$[1, 0, 0, 20318861969, -7362840722038855]$	\(y^2+xy=x^3+20318861969x-7362840722038855\)	1720.2.0.?	$[ ]$
277350.be1	277350be1	277350.be	277350be	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 43^{2} \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{15} \cdot 43^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$52.59934639$	$1$		$0$	$47389224960$	$6.679787$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$8.25241$	$[1, 0, 1, 5557629553349, 33306640876850888198]$	\(y^2+xy+y=x^3+5557629553349x+33306640876850888198\)	1720.2.0.?	$[(-32980419688295902998607298/4448854411, 388097219395081726481766437056590797636/4448854411)]$
316050.jn1	316050jn1	316050.jn	316050jn	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{15} \cdot 7^{6} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$1$		$0$	$8462361600$	$5.772141$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.30721$	$[1, 0, 0, 147281691787, 143687708475120417]$	\(y^2+xy=x^3+147281691787x+143687708475120417\)	1720.2.0.?	$[ ]$
372810.k1	372810k1	372810.k	372810k	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 17^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{9} \cdot 17^{6} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$1$		$0$	$5539000320$	$5.411079$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$6.87539$	$[1, 1, 0, 34746456267, -16465003631667027]$	\(y^2+xy=x^3+x^2+34746456267x-16465003631667027\)	1720.2.0.?	$[ ]$
443760.br1	443760br1	443760.br	443760br	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5 \cdot 43^{2} \)	\( - 2^{65} \cdot 3^{8} \cdot 5^{9} \cdot 43^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1$	$1$		$0$	$47389224960$	$6.568214$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.85115$	$[0, 1, 0, 3556882914144, -17052998706194489100]$	\(y^2=x^3+x^2+3556882914144x-17052998706194489100\)	1720.2.0.?	$[ ]$
465690.bu1	465690bu1	465690.bu	465690bu	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 19^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{8} \cdot 5^{9} \cdot 19^{6} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$1.616444072$	$1$		$4$	$6750656640$	$5.466690$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$6.80934$	$[1, 1, 1, 43403012845, 22986698160322577]$	\(y^2+xy+y=x^3+x^2+43403012845x+22986698160322577\)	1720.2.0.?	$[(8896227, 26537631886)]$
468270.ba1	468270ba1	468270.ba	468270ba	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 43 \)	\( - 2^{53} \cdot 3^{14} \cdot 5^{9} \cdot 11^{6} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$505.9888380$	$1$		$0$	$10941235200$	$5.742722$	$192203697666261893287480365959/4963160303408775168000000000$	$1.09175$	$7.06015$	$[1, -1, 0, 130930418250, -120436294852687500]$	\(y^2+xy=x^3-x^2+130930418250x-120436294852687500\)	1720.2.0.?	$[(174992003668085976860464442158522498941993638638662069775718284913409643035546323062408887292984808999579520515894563255703143160616458874871286092733254609082754341079079329372350199306707805725011255002457415981079842019/179427923603057170230277405133776396209211456672751364021253551826371069653881943650451507778424307005734523, 73321660791220339097611718423922035723065151317327242645966081841662568404394158874009395994101309321437187106013150210097247648058684066747459665517328999937541073996980498833690436897849357997086517526476054261829551608189874118905971543579502338744892743024966314609437507944091092010562387718016328451178243352153821475177865043/179427923603057170230277405133776396209211456672751364021253551826371069653881943650451507778424307005734523)]$

  Download displayed columns for results to