LMFDB - Elliptic curve search results

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

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Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (24 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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
9702.f1	9702f1	9702.f	9702f	$1$	$1$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{9} \cdot 7^{10} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$1$		$0$	$423360$	$2.768845$	$-34068278205171/10307264$	$1.07746$	$6.59106$	$[1, -1, 0, -11964633, 15936473069]$	$y^2+xy=x^3-x^2-11964633x+15936473069$	132.2.0.?	$[]$
9702.s1	9702a1	9702.s	9702a	$1$	$1$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{9} \cdot 7^{4} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$8.770756740$	$1$		$2$	$60480$	$1.795891$	$-34068278205171/10307264$	$1.07746$	$5.31924$	$[1, -1, 0, -244176, -46392256]$	$y^2+xy=x^3-x^2-244176x-46392256$	132.2.0.?	$[(94408, 28959976)]$
9702.bi1	9702bd1	9702.bi	9702bd	$1$	$1$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{3} \cdot 7^{4} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$0.112262414$	$1$		$10$	$20160$	$1.246586$	$-34068278205171/10307264$	$1.07746$	$4.60120$	$[1, -1, 1, -27131, 1727275]$	$y^2+xy+y=x^3-x^2-27131x+1727275$	132.2.0.?	$[(73, 326)]$
9702.ca1	9702bi1	9702.ca	9702bi	$1$	$1$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{3} \cdot 7^{10} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$1$		$0$	$141120$	$2.219540$	$-34068278205171/10307264$	$1.07746$	$5.87302$	$[1, -1, 1, -1329404, -589796609]$	$y^2+xy+y=x^3-x^2-1329404x-589796609$	132.2.0.?	$[]$
77616.bk1	77616cu1	77616.bk	77616cu	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{18} \cdot 3^{3} \cdot 7^{4} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$1$		$0$	$483840$	$1.939732$	$-34068278205171/10307264$	$1.07746$	$4.49017$	$[0, 0, 0, -434091, -110111526]$	$y^2=x^3-434091x-110111526$	132.2.0.?	$[]$
77616.bv1	77616dw1	77616.bv	77616dw	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{18} \cdot 3^{9} \cdot 7^{10} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$1$		$0$	$10160640$	$3.461994$	$-34068278205171/10307264$	$1.07746$	$6.11254$	$[0, 0, 0, -191434131, -1019742842286]$	$y^2=x^3-191434131x-1019742842286$	132.2.0.?	$[]$
77616.fc1	77616dg1	77616.fc	77616dg	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{18} \cdot 3^{3} \cdot 7^{10} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$10.62910388$	$1$		$0$	$3386880$	$2.912685$	$-34068278205171/10307264$	$1.07746$	$5.52711$	$[0, 0, 0, -21270459, 37768253418]$	$y^2=x^3-21270459x+37768253418$	132.2.0.?	$[(292359/11, 29174034/11)]$
77616.fu1	77616cy1	77616.fu	77616cy	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{18} \cdot 3^{9} \cdot 7^{4} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$0.543449398$	$1$		$6$	$1451520$	$2.489037$	$-34068278205171/10307264$	$1.07746$	$5.07560$	$[0, 0, 0, -3906819, 2973011202]$	$y^2=x^3-3906819x+2973011202$	132.2.0.?	$[(1071, 4158)]$
106722.t1	106722h1	106722.t	106722h	$1$	$1$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 7^{4} \cdot 11^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$1$		$0$	$2419200$	$2.445534$	$-34068278205171/10307264$	$1.07746$	$4.89090$	$[1, -1, 0, -3282813, -2289154939]$	$y^2+xy=x^3-x^2-3282813x-2289154939$	132.2.0.?	$[]$
106722.dh1	106722w1	106722.dh	106722w	$1$	$1$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 7^{10} \cdot 11^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$7.220668024$	$1$		$2$	$16934400$	$3.418488$	$-34068278205171/10307264$	$1.07746$	$5.89932$	$[1, -1, 0, -160857846, 785501859764]$	$y^2+xy=x^3-x^2-160857846x+785501859764$	132.2.0.?	$[(3868, 468346)]$
106722.ey1	106722ez1	106722.ey	106722ez	$1$	$1$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{6} \cdot 3^{9} \cdot 7^{10} \cdot 11^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$4$	$2$	$0$	$50803200$	$3.967793$	$-34068278205171/10307264$	$1.07746$	$6.46865$	$[1, -1, 1, -1447720616, -21207102493013]$	$y^2+xy+y=x^3-x^2-1447720616x-21207102493013$	132.2.0.?	$[]$
106722.gr1	106722ef1	106722.gr	106722ef	$1$	$1$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{6} \cdot 3^{9} \cdot 7^{4} \cdot 11^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$0.573202955$	$1$		$4$	$7257600$	$2.994839$	$-34068278205171/10307264$	$1.07746$	$5.46023$	$[1, -1, 1, -29545319, 61836728671]$	$y^2+xy+y=x^3-x^2-29545319x+61836728671$	132.2.0.?	$[(5063, 202442)]$
242550.fa1	242550fa1	242550.fa	242550fa	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 7^{4} \cdot 11^{5} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$0.228754115$	$1$		$22$	$2580480$	$2.051304$	$-34068278205171/10307264$	$1.07746$	$4.18551$	$[1, -1, 0, -678267, 215231141]$	$y^2+xy=x^3-x^2-678267x+215231141$	132.2.0.?	$[(254, 7573), (-362, 20509)]$
242550.gp1	242550gp1	242550.gp	242550gp	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 7^{10} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$5.292705165$	$1$		$2$	$18063360$	$3.024258$	$-34068278205171/10307264$	$1.07746$	$5.12716$	$[1, -1, 0, -33235092, -73757811184]$	$y^2+xy=x^3-x^2-33235092x-73757811184$	132.2.0.?	$[(15824, 1825788)]$
242550.iz1	242550iz1	242550.iz	242550iz	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 7^{4} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$1$		$0$	$7741440$	$2.600609$	$-34068278205171/10307264$	$1.07746$	$4.71714$	$[1, -1, 1, -6104405, -5805136403]$	$y^2+xy+y=x^3-x^2-6104405x-5805136403$	132.2.0.?	$[]$
242550.kc1	242550kc1	242550.kc	242550kc	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 7^{10} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$6.204629806$	$1$		$2$	$54190080$	$3.573566$	$-34068278205171/10307264$	$1.07746$	$5.65879$	$[1, -1, 1, -299115830, 1991760017797]$	$y^2+xy+y=x^3-x^2-299115830x+1991760017797$	132.2.0.?	$[(35629, 6028835)]$
310464.co1	310464co1	310464.co	310464co	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{24} \cdot 3^{9} \cdot 7^{4} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$1$		$0$	$11612160$	$2.835613$	$-34068278205171/10307264$	$1.07746$	$4.84806$	$[0, 0, 0, -15627276, 23784089616]$	$y^2=x^3-15627276x+23784089616$	132.2.0.?	$[]$
310464.dd1	310464dd1	310464.dd	310464dd	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{24} \cdot 3^{3} \cdot 7^{10} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$4$	$2$	$0$	$27095040$	$3.259262$	$-34068278205171/10307264$	$1.07746$	$5.25007$	$[0, 0, 0, -85081836, -302146027344]$	$y^2=x^3-85081836x-302146027344$	132.2.0.?	$[]$
310464.eh1	310464eh1	310464.eh	310464eh	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{24} \cdot 3^{9} \cdot 7^{4} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$1$		$0$	$11612160$	$2.835613$	$-34068278205171/10307264$	$1.07746$	$4.84806$	$[0, 0, 0, -15627276, -23784089616]$	$y^2=x^3-15627276x-23784089616$	132.2.0.?	$[]$
310464.ew1	310464ew1	310464.ew	310464ew	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{24} \cdot 3^{3} \cdot 7^{10} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$1$	$1$		$0$	$27095040$	$3.259262$	$-34068278205171/10307264$	$1.07746$	$5.25007$	$[0, 0, 0, -85081836, 302146027344]$	$y^2=x^3-85081836x+302146027344$	132.2.0.?	$[]$
310464.nc1	310464nc1	310464.nc	310464nc	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{24} \cdot 3^{3} \cdot 7^{4} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$3.664513344$	$1$		$2$	$3870720$	$2.286304$	$-34068278205171/10307264$	$1.07746$	$4.32681$	$[0, 0, 0, -1736364, 880892208]$	$y^2=x^3-1736364x+880892208$	132.2.0.?	$[(214, 22784)]$
310464.nq1	310464nq1	310464.nq	310464nq	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{24} \cdot 3^{9} \cdot 7^{10} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$174.5723876$	$1$		$0$	$81285120$	$3.808567$	$-34068278205171/10307264$	$1.07746$	$5.77133$	$[0, 0, 0, -765736524, -8157942738288]$	$y^2=x^3-765736524x-8157942738288$	132.2.0.?	$[(45383859702682354662859712497472184222473496549448649775961088318466176616384/1189867603013546746212019505769345647, 816732949292147495549132680560837288163636174529913940428982305474974116298236897024693241724923493877790556595116/1189867603013546746212019505769345647)]$
310464.ot1	310464ot1	310464.ot	310464ot	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{24} \cdot 3^{3} \cdot 7^{4} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$2.347869574$	$1$		$2$	$3870720$	$2.286304$	$-34068278205171/10307264$	$1.07746$	$4.32681$	$[0, 0, 0, -1736364, -880892208]$	$y^2=x^3-1736364x-880892208$	132.2.0.?	$[(1596, 20328)]$
310464.ph1	310464ph1	310464.ph	310464ph	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{24} \cdot 3^{9} \cdot 7^{10} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$132$	$2$	$0$	$3.774031299$	$1$		$2$	$81285120$	$3.808567$	$-34068278205171/10307264$	$1.07746$	$5.77133$	$[0, 0, 0, -765736524, 8157942738288]$	$y^2=x^3-765736524x+8157942738288$	132.2.0.?	$[(-14706, 4029696)]$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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