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	Manin constant

Intrinsic torsion order

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Results (20 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
4158.j1	4158g1	4158.j	4158g	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7 \cdot 11 $	$ - 2^{21} \cdot 3^{9} \cdot 7 \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$12096$	$1.294659$	$-1802929676211/1776287744$	$0.98533$	$4.69256$	$1$	$[1, -1, 0, -6846, -356716]$	$y^2+xy=x^3-x^2-6846x-356716$	168.2.0.?	$[ ]$	$1$
4158.s1	4158t1	4158.s	4158t	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7 \cdot 11 $	$ - 2^{21} \cdot 3^{3} \cdot 7 \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$0.109292213$	$1$		$8$	$4032$	$0.745352$	$-1802929676211/1776287744$	$0.98533$	$3.90151$	$1$	$[1, -1, 1, -761, 13465]$	$y^2+xy+y=x^3-x^2-761x+13465$	168.2.0.?	$[(23, 76)]$	$1$
29106.g1	29106j1	29106.g	29106j	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7^{2} \cdot 11 $	$ - 2^{21} \cdot 3^{9} \cdot 7^{7} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$580608$	$2.267612$	$-1802929676211/1776287744$	$0.98533$	$4.94008$	$1$	$[1, -1, 0, -335463, 123024509]$	$y^2+xy=x^3-x^2-335463x+123024509$	168.2.0.?	$[ ]$	$1$
29106.cq1	29106cu1	29106.cq	29106cu	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7^{2} \cdot 11 $	$ - 2^{21} \cdot 3^{3} \cdot 7^{7} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$0.707281148$	$1$		$4$	$193536$	$1.718307$	$-1802929676211/1776287744$	$0.98533$	$4.29878$	$1$	$[1, -1, 1, -37274, -4544039]$	$y^2+xy+y=x^3-x^2-37274x-4544039$	168.2.0.?	$[(1073, 33959)]$	$1$
33264.i1	33264bi1	33264.i	33264bi	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 7 \cdot 11 $	$ - 2^{33} \cdot 3^{3} \cdot 7 \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$96768$	$1.438499$	$-1802929676211/1776287744$	$0.98533$	$3.92118$	$1$	$[0, 0, 0, -12171, -849606]$	$y^2=x^3-12171x-849606$	168.2.0.?	$[ ]$	$1$
33264.bj1	33264bc1	33264.bj	33264bc	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 7 \cdot 11 $	$ - 2^{33} \cdot 3^{9} \cdot 7 \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$290304$	$1.987806$	$-1802929676211/1776287744$	$0.98533$	$4.55425$	$1$	$[0, 0, 0, -109539, 22939362]$	$y^2=x^3-109539x+22939362$	168.2.0.?	$[ ]$	$1$
45738.l1	45738w1	45738.l	45738w	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7 \cdot 11^{2} $	$ - 2^{21} \cdot 3^{3} \cdot 7 \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$11.89879981$	$1$		$0$	$483840$	$1.944300$	$-1802929676211/1776287744$	$0.98533$	$4.37044$	$1$	$[1, -1, 0, -92043, -17646139]$	$y^2+xy=x^3-x^2-92043x-17646139$	168.2.0.?	$[(1063481/53, 163970654/53)]$	$1$
45738.di1	45738dl1	45738.di	45738dl	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7 \cdot 11^{2} $	$ - 2^{21} \cdot 3^{9} \cdot 7 \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$0.503456338$	$1$		$6$	$1451520$	$2.493607$	$-1802929676211/1776287744$	$0.98533$	$4.98472$	$1$	$[1, -1, 1, -828389, 477274141]$	$y^2+xy+y=x^3-x^2-828389x+477274141$	168.2.0.?	$[(223, 17312)]$	$1$
103950.do1	103950da1	103950.do	103950da	$1$	$1$	$ 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{21} \cdot 3^{3} \cdot 5^{6} \cdot 7 \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$516096$	$1.550072$	$-1802929676211/1776287744$	$0.98533$	$3.65030$	$1$	$[1, -1, 0, -19017, 1664141]$	$y^2+xy=x^3-x^2-19017x+1664141$	168.2.0.?	$[ ]$	$1$
103950.gr1	103950fa1	103950.gr	103950fa	$1$	$1$	$ 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{21} \cdot 3^{9} \cdot 5^{6} \cdot 7 \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1.245699563$	$1$		$4$	$1548288$	$2.099377$	$-1802929676211/1776287744$	$0.98533$	$4.22093$	$1$	$[1, -1, 1, -171155, -44760653]$	$y^2+xy+y=x^3-x^2-171155x-44760653$	168.2.0.?	$[(539, 4130)]$	$1$
133056.ba1	133056dk1	133056.ba	133056dk	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7 \cdot 11 $	$ - 2^{39} \cdot 3^{9} \cdot 7 \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$2322432$	$2.334377$	$-1802929676211/1776287744$	$0.98533$	$4.37163$	$1$	$[0, 0, 0, -438156, -183514896]$	$y^2=x^3-438156x-183514896$	168.2.0.?	$[ ]$	$1$
133056.bc1	133056h1	133056.bc	133056h	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7 \cdot 11 $	$ - 2^{39} \cdot 3^{9} \cdot 7 \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$2322432$	$2.334377$	$-1802929676211/1776287744$	$0.98533$	$4.37163$	$1$	$[0, 0, 0, -438156, 183514896]$	$y^2=x^3-438156x+183514896$	168.2.0.?	$[ ]$	$1$
133056.dl1	133056cu1	133056.dl	133056cu	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7 \cdot 11 $	$ - 2^{39} \cdot 3^{3} \cdot 7 \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$774144$	$1.785072$	$-1802929676211/1776287744$	$0.98533$	$3.81294$	$1$	$[0, 0, 0, -48684, 6796848]$	$y^2=x^3-48684x+6796848$	168.2.0.?	$[ ]$	$1$
133056.dr1	133056br1	133056.dr	133056br	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7 \cdot 11 $	$ - 2^{39} \cdot 3^{3} \cdot 7 \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$4$	$2$	$0$	$774144$	$1.785072$	$-1802929676211/1776287744$	$0.98533$	$3.81294$	$1$	$[0, 0, 0, -48684, -6796848]$	$y^2=x^3-48684x-6796848$	168.2.0.?	$[ ]$	$1$
232848.bo1	232848bo1	232848.bo	232848bo	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 7^{2} \cdot 11 $	$ - 2^{33} \cdot 3^{9} \cdot 7^{7} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1.208093995$	$1$		$4$	$13934592$	$2.960762$	$-1802929676211/1776287744$	$0.98533$	$4.78190$	$1$	$[0, 0, 0, -5367411, -7868201166]$	$y^2=x^3-5367411x-7868201166$	168.2.0.?	$[(23625, 3612672)]$	$1$
232848.ex1	232848ex1	232848.ex	232848ex	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 7^{2} \cdot 11 $	$ - 2^{33} \cdot 3^{3} \cdot 7^{7} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$3.165477894$	$1$		$2$	$4644864$	$2.411453$	$-1802929676211/1776287744$	$0.98533$	$4.24851$	$1$	$[0, 0, 0, -596379, 291414858]$	$y^2=x^3-596379x+291414858$	168.2.0.?	$[(406, 10780)]$	$1$
320166.dj1	320166dj1	320166.dj	320166dj	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{21} \cdot 3^{3} \cdot 7^{7} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$23224320$	$2.917255$	$-1802929676211/1776287744$	$0.98533$	$4.62058$	$1$	$[1, -1, 0, -4510116, 6061645904]$	$y^2+xy=x^3-x^2-4510116x+6061645904$	168.2.0.?	$[ ]$	$1$
320166.fi1	320166fi1	320166.fi	320166fi	$1$	$1$	$ 2 \cdot 3^{3} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{21} \cdot 3^{9} \cdot 7^{7} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$69672960$	$3.466560$	$-1802929676211/1776287744$	$0.98533$	$5.14057$	$1$	$[1, -1, 1, -40591046, -163623848363]$	$y^2+xy+y=x^3-x^2-40591046x-163623848363$	168.2.0.?	$[ ]$	$1$
365904.bq1	365904bq1	365904.bq	365904bq	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 7 \cdot 11^{2} $	$ - 2^{33} \cdot 3^{3} \cdot 7 \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$1$	$1$		$0$	$11612160$	$2.637447$	$-1802929676211/1776287744$	$0.98533$	$4.31031$	$1$	$[0, 0, 0, -1472691, 1130825586]$	$y^2=x^3-1472691x+1130825586$	168.2.0.?	$[ ]$	$1$
365904.gn1	365904gn1	365904.gn	365904gn	$1$	$1$	$ 2^{4} \cdot 3^{3} \cdot 7 \cdot 11^{2} $	$ - 2^{33} \cdot 3^{9} \cdot 7 \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$168$	$2$	$0$	$65.07090820$	$1$		$0$	$34836480$	$3.186752$	$-1802929676211/1776287744$	$0.98533$	$4.82487$	$1$	$[0, 0, 0, -13254219, -30532290822]$	$y^2=x^3-13254219x-30532290822$	168.2.0.?	$[(398085345246643952761080891751/974316508873, 251158469660095143977684980574409325225739042/974316508873)]$	$1$

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Results (20 matches)

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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