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

Galois image	Adelic level	Adelic index	Adelic genus

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

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Results (30 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
5544.a1	5544k1	5544.a	5544k	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 7^{3} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.134119078$	$1$		$8$	$7680$	$1.030796$	$-610325920583424/55240493$	$1.08372$	$4.65329$	$[0, 0, 0, -13359, 594351]$	$y^2=x^3-13359x+594351$	462.2.0.?	$[(69, 33)]$
5544.v1	5544a1	5544.v	5544a	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 7^{3} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$8.661651070$	$1$		$0$	$23040$	$1.580103$	$-610325920583424/55240493$	$1.08372$	$5.41795$	$[0, 0, 0, -120231, -16047477]$	$y^2=x^3-120231x-16047477$	462.2.0.?	$[(32643/7, 4844799/7)]$
11088.e1	11088g1	11088.e	11088g	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 7^{3} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$15360$	$1.030796$	$-610325920583424/55240493$	$1.08372$	$4.30698$	$[0, 0, 0, -13359, -594351]$	$y^2=x^3-13359x-594351$	462.2.0.?	$[]$
11088.bx1	11088h1	11088.bx	11088h	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 7^{3} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.283458966$	$1$		$4$	$46080$	$1.580103$	$-610325920583424/55240493$	$1.08372$	$5.01473$	$[0, 0, 0, -120231, 16047477]$	$y^2=x^3-120231x+16047477$	462.2.0.?	$[(108, 2079)]$
38808.h1	38808j1	38808.h	38808j	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 7^{9} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$1105920$	$2.553059$	$-610325920583424/55240493$	$1.08372$	$5.52514$	$[0, 0, 0, -5891319, 5504284611]$	$y^2=x^3-5891319x+5504284611$	462.2.0.?	$[]$
38808.cn1	38808by1	38808.cn	38808by	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 7^{9} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$368640$	$2.003750$	$-610325920583424/55240493$	$1.08372$	$4.90130$	$[0, 0, 0, -654591, -203862393]$	$y^2=x^3-654591x-203862393$	462.2.0.?	$[]$
44352.p1	44352e1	44352.p	44352e	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{9} \cdot 7^{3} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$368640$	$1.926676$	$-610325920583424/55240493$	$1.08372$	$4.75370$	$[0, 0, 0, -480924, -128379816]$	$y^2=x^3-480924x-128379816$	462.2.0.?	$[]$
44352.r1	44352dd1	44352.r	44352dd	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{9} \cdot 7^{3} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1.575053391$	$1$		$2$	$368640$	$1.926676$	$-610325920583424/55240493$	$1.08372$	$4.75370$	$[0, 0, 0, -480924, 128379816]$	$y^2=x^3-480924x+128379816$	462.2.0.?	$[(405, 189)]$
44352.er1	44352b1	44352.er	44352b	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{3} \cdot 7^{3} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$4.683125878$	$1$		$2$	$122880$	$1.377371$	$-610325920583424/55240493$	$1.08372$	$4.13765$	$[0, 0, 0, -53436, 4754808]$	$y^2=x^3-53436x+4754808$	462.2.0.?	$[(-3, 2217)]$
44352.ex1	44352dg1	44352.ex	44352dg	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{3} \cdot 7^{3} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$122880$	$1.377371$	$-610325920583424/55240493$	$1.08372$	$4.13765$	$[0, 0, 0, -53436, -4754808]$	$y^2=x^3-53436x-4754808$	462.2.0.?	$[]$
60984.e1	60984l1	60984.e	60984l	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{3} \cdot 7^{3} \cdot 11^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1.356016321$	$1$		$2$	$921600$	$2.229744$	$-610325920583424/55240493$	$1.08372$	$4.94637$	$[0, 0, 0, -1616439, -791081181]$	$y^2=x^3-1616439x-791081181$	462.2.0.?	$[(4686, 307461)]$
60984.ci1	60984bu1	60984.ci	60984bu	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{9} \cdot 7^{3} \cdot 11^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$2764800$	$2.779049$	$-610325920583424/55240493$	$1.08372$	$5.54462$	$[0, 0, 0, -14547951, 21359191887]$	$y^2=x^3-14547951x+21359191887$	462.2.0.?	$[]$
77616.bc1	77616bd1	77616.bc	77616bd	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 7^{9} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$2.777270929$	$1$		$0$	$2211840$	$2.553059$	$-610325920583424/55240493$	$1.08372$	$5.18501$	$[0, 0, 0, -5891319, -5504284611]$	$y^2=x^3-5891319x-5504284611$	462.2.0.?	$[(11529/2, 305613/2)]$
77616.gg1	77616p1	77616.gg	77616p	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 7^{9} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$737280$	$2.003750$	$-610325920583424/55240493$	$1.08372$	$4.59958$	$[0, 0, 0, -654591, 203862393]$	$y^2=x^3-654591x+203862393$	462.2.0.?	$[]$
121968.l1	121968j1	121968.l	121968j	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{3} \cdot 7^{3} \cdot 11^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$1843200$	$2.229744$	$-610325920583424/55240493$	$1.08372$	$4.65362$	$[0, 0, 0, -1616439, 791081181]$	$y^2=x^3-1616439x+791081181$	462.2.0.?	$[]$
121968.fo1	121968i1	121968.fo	121968i	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{9} \cdot 7^{3} \cdot 11^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$16$	$2$	$0$	$5529600$	$2.779049$	$-610325920583424/55240493$	$1.08372$	$5.21646$	$[0, 0, 0, -14547951, -21359191887]$	$y^2=x^3-14547951x-21359191887$	462.2.0.?	$[]$
138600.dn1	138600ch1	138600.dn	138600ch	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 5^{6} \cdot 7^{3} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$11.16044149$	$1$		$0$	$2488320$	$2.384823$	$-610325920583424/55240493$	$1.08372$	$4.76056$	$[0, 0, 0, -3005775, -2005934625]$	$y^2=x^3-3005775x-2005934625$	462.2.0.?	$[(1721061/13, 2222709741/13)]$
138600.eq1	138600eu1	138600.eq	138600eu	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 5^{6} \cdot 7^{3} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.256588816$	$1$		$6$	$829440$	$1.835516$	$-610325920583424/55240493$	$1.08372$	$4.20380$	$[0, 0, 0, -333975, 74293875]$	$y^2=x^3-333975x+74293875$	462.2.0.?	$[(411, 2541)]$
277200.cn1	277200cn1	277200.cn	277200cn	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 5^{6} \cdot 7^{3} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$33.23475824$	$1$		$0$	$1658880$	$1.835516$	$-610325920583424/55240493$	$1.08372$	$3.97129$	$[0, 0, 0, -333975, -74293875]$	$y^2=x^3-333975x-74293875$	462.2.0.?	$[(428902706752476/351581, 8750481581968021758399/351581)]$
277200.gc1	277200gc1	277200.gc	277200gc	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 5^{6} \cdot 7^{3} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$4976640$	$2.384823$	$-610325920583424/55240493$	$1.08372$	$4.49726$	$[0, 0, 0, -3005775, 2005934625]$	$y^2=x^3-3005775x+2005934625$	462.2.0.?	$[]$
310464.bc1	310464bc1	310464.bc	310464bc	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{3} \cdot 7^{9} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$5898240$	$2.350327$	$-610325920583424/55240493$	$1.08372$	$4.42422$	$[0, 0, 0, -2618364, -1630899144]$	$y^2=x^3-2618364x-1630899144$	462.2.0.?	$[]$
310464.br1	310464br1	310464.br	310464br	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{3} \cdot 7^{9} \cdot 11^{5} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.939927161$	$1$		$8$	$5898240$	$2.350327$	$-610325920583424/55240493$	$1.08372$	$4.42422$	$[0, 0, 0, -2618364, 1630899144]$	$y^2=x^3-2618364x+1630899144$	462.2.0.?	$[(-35, 41503), (3633/2, 11319/2)]$
310464.py1	310464py1	310464.py	310464py	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{9} \cdot 7^{9} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$38.42995034$	$1$		$0$	$17694720$	$2.899632$	$-610325920583424/55240493$	$1.08372$	$4.94548$	$[0, 0, 0, -23565276, -44034276888]$	$y^2=x^3-23565276x-44034276888$	462.2.0.?	$[(1307635974299311573/7731041, 1454805671064692190334501859/7731041)]$
310464.qu1	310464qu1	310464.qu	310464qu	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{9} \cdot 7^{9} \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$3.349214116$	$1$		$2$	$17694720$	$2.899632$	$-610325920583424/55240493$	$1.08372$	$4.94548$	$[0, 0, 0, -23565276, 44034276888]$	$y^2=x^3-23565276x+44034276888$	462.2.0.?	$[(2997, 18117)]$
426888.r1	426888r1	426888.r	426888r	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{4} \cdot 3^{9} \cdot 7^{9} \cdot 11^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$		$0$	$132710400$	$3.752007$	$-610325920583424/55240493$	$1.08372$	$5.61297$	$[0, 0, 0, -712849599, -7326202817241]$	$y^2=x^3-712849599x-7326202817241$	462.2.0.?	$[]$
426888.hf1	426888hf1	426888.hf	426888hf	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{4} \cdot 3^{3} \cdot 7^{9} \cdot 11^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1.342574213$	$1$		$4$	$44236800$	$3.202698$	$-610325920583424/55240493$	$1.08372$	$5.10452$	$[0, 0, 0, -79205511, 271340845083]$	$y^2=x^3-79205511x+271340845083$	462.2.0.?	$[(5467, 41503)]$
487872.bf1	487872bf1	487872.bf	487872bf	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{9} \cdot 7^{3} \cdot 11^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$39.09257331$	$1$		$0$	$44236800$	$3.125626$	$-610325920583424/55240493$	$1.08372$	$4.98187$	$[0, 0, 0, -58191804, -170873535096]$	$y^2=x^3-58191804x-170873535096$	462.2.0.?	$[(3956054042346845373/18290897, 5454179540974628658347715441/18290897)]$
487872.cl1	487872cl1	487872.cl	487872cl	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{9} \cdot 7^{3} \cdot 11^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1.836670913$	$1$		$0$	$44236800$	$3.125626$	$-610325920583424/55240493$	$1.08372$	$4.98187$	$[0, 0, 0, -58191804, 170873535096]$	$y^2=x^3-58191804x+170873535096$	462.2.0.?	$[(19305/2, 395307/2)]$
487872.os1	487872os1	487872.os	487872os	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{3} \cdot 7^{3} \cdot 11^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$4.834330233$	$1$		$0$	$14745600$	$2.576317$	$-610325920583424/55240493$	$1.08372$	$4.47860$	$[0, 0, 0, -6465756, 6328649448]$	$y^2=x^3-6465756x+6328649448$	462.2.0.?	$[(-18183/4, 7071603/4)]$
487872.pq1	487872pq1	487872.pq	487872pq	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{3} \cdot 7^{3} \cdot 11^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$17.84149984$	$1$		$0$	$14745600$	$2.576317$	$-610325920583424/55240493$	$1.08372$	$4.47860$	$[0, 0, 0, -6465756, -6328649448]$	$y^2=x^3-6465756x-6328649448$	462.2.0.?	$[(2639728773/929, 40162639315491/929)]$

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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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