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

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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	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
5850.i1	5850a2	5850.i	5850a	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2 \cdot 3^{9} \cdot 5^{10} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$13.55854540$	$1$		$0$	$38880$	$1.663858$	$-8538302475/26$	$0.97351$	$5.63161$	$[1, -1, 0, -245742, -46827334]$	$y^2+xy=x^3-x^2-245742x-46827334$	3.4.0.a.1, 15.8.0-3.a.1.1, 312.8.0.?, 1560.16.0.?	$[(3743875/31, 7123548589/31)]$
5850.r1	5850g1	5850.r	5850g	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2 \cdot 3^{3} \cdot 5^{4} \cdot 13 $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$312$	$16$	$0$	$1.703561494$	$1$		$6$	$2592$	$0.309834$	$-8538302475/26$	$0.97351$	$3.75844$	$[1, -1, 0, -1092, 14166]$	$y^2+xy=x^3-x^2-1092x+14166$	3.8.0-3.a.1.2, 312.16.0.?	$[(15, 24)]$
5850.bg1	5850bc1	5850.bg	5850bc	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2 \cdot 3^{3} \cdot 5^{10} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$		$0$	$12960$	$1.114552$	$-8538302475/26$	$0.97351$	$4.87170$	$[1, -1, 1, -27305, 1743447]$	$y^2+xy+y=x^3-x^2-27305x+1743447$	3.4.0.a.1, 15.8.0-3.a.1.2, 312.8.0.?, 1560.16.0.?	$[ ]$
5850.bx1	5850bi2	5850.bx	5850bi	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2 \cdot 3^{9} \cdot 5^{4} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$312$	$16$	$0$	$1$	$9$	$3$	$0$	$7776$	$0.859139$	$-8538302475/26$	$0.97351$	$4.51835$	$[1, -1, 1, -9830, -372653]$	$y^2+xy+y=x^3-x^2-9830x-372653$	3.8.0-3.a.1.1, 312.16.0.?	$[ ]$
46800.bf1	46800cs2	46800.bf	46800cs	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{9} \cdot 5^{4} \cdot 13 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1.474526596$	$1$		$12$	$186624$	$1.552286$	$-8538302475/26$	$0.97351$	$4.41812$	$[0, 0, 0, -157275, 24007050]$	$y^2=x^3-157275x+24007050$	3.4.0.a.1, 12.8.0-3.a.1.2, 312.16.0.?	$[(231, 54), (229, 8)]$
46800.bt1	46800cr1	46800.bt	46800cr	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{3} \cdot 5^{4} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1$	$1$		$0$	$62208$	$1.002981$	$-8538302475/26$	$0.97351$	$3.80515$	$[0, 0, 0, -17475, -889150]$	$y^2=x^3-17475x-889150$	3.4.0.a.1, 12.8.0-3.a.1.1, 312.16.0.?	$[ ]$
46800.du1	46800ca2	46800.du	46800ca	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{9} \cdot 5^{10} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$		$0$	$933120$	$2.357006$	$-8538302475/26$	$0.97351$	$5.31611$	$[0, 0, 0, -3931875, 3000881250]$	$y^2=x^3-3931875x+3000881250$	3.4.0.a.1, 60.8.0-3.a.1.1, 312.8.0.?, 1560.16.0.?	$[ ]$
46800.ep1	46800bz1	46800.ep	46800bz	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{3} \cdot 5^{10} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$4$	$2$	$0$	$311040$	$1.807699$	$-8538302475/26$	$0.97351$	$4.70314$	$[0, 0, 0, -436875, -111143750]$	$y^2=x^3-436875x-111143750$	3.4.0.a.1, 60.8.0-3.a.1.2, 312.8.0.?, 1560.16.0.?	$[ ]$
76050.v1	76050t2	76050.v	76050t	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{9} \cdot 5^{4} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1$	$1$		$0$	$1306368$	$2.141613$	$-8538302475/26$	$0.97351$	$4.85649$	$[1, -1, 0, -1661217, -823701709]$	$y^2+xy=x^3-x^2-1661217x-823701709$	3.4.0.a.1, 24.8.0-3.a.1.6, 39.8.0-3.a.1.2, 312.16.0.?	$[ ]$
76050.cq1	76050g1	76050.cq	76050g	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{3} \cdot 5^{10} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$2.362375948$	$1$		$0$	$2177280$	$2.397026$	$-8538302475/26$	$0.97351$	$5.12919$	$[1, -1, 0, -4614492, 3816510166]$	$y^2+xy=x^3-x^2-4614492x+3816510166$	3.4.0.a.1, 120.8.0.?, 195.8.0.?, 312.8.0.?, 1560.16.0.?	$[(4967/2, -3953/2)]$
76050.eg1	76050dx1	76050.eg	76050dx	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{3} \cdot 5^{4} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$3.598614727$	$1$		$0$	$435456$	$1.592308$	$-8538302475/26$	$0.97351$	$4.27000$	$[1, -1, 1, -184580, 30568997]$	$y^2+xy+y=x^3-x^2-184580x+30568997$	3.4.0.a.1, 24.8.0-3.a.1.5, 39.8.0-3.a.1.1, 312.16.0.?	$[(4125/4, 8449/4)]$
76050.fh1	76050dl2	76050.fh	76050dl	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2 \cdot 3^{9} \cdot 5^{10} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$9$	$3$	$0$	$6531840$	$2.946335$	$-8538302475/26$	$0.97351$	$5.71568$	$[1, -1, 1, -41530430, -103004244053]$	$y^2+xy+y=x^3-x^2-41530430x-103004244053$	3.4.0.a.1, 120.8.0.?, 195.8.0.?, 312.8.0.?, 1560.16.0.?	$[ ]$
187200.dk1	187200gq1	187200.dk	187200gq	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{19} \cdot 3^{3} \cdot 5^{4} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$8.206280647$	$1$		$0$	$497664$	$1.349554$	$-8538302475/26$	$0.97351$	$3.71321$	$[0, 0, 0, -69900, -7113200]$	$y^2=x^3-69900x-7113200$	3.4.0.a.1, 24.8.0-3.a.1.4, 156.8.0.?, 312.16.0.?	$[(8876/5, 447624/5)]$
187200.dm1	187200pe2	187200.dm	187200pe	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{19} \cdot 3^{9} \cdot 5^{10} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$9$	$3$	$0$	$7464960$	$2.703579$	$-8538302475/26$	$0.97351$	$5.05162$	$[0, 0, 0, -15727500, -24007050000]$	$y^2=x^3-15727500x-24007050000$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 390.8.0.?, 1560.16.0.?	$[ ]$
187200.fn1	187200gv2	187200.fn	187200gv	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{19} \cdot 3^{9} \cdot 5^{4} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$0.533974571$	$1$		$4$	$1492992$	$1.898861$	$-8538302475/26$	$0.97351$	$4.25618$	$[0, 0, 0, -629100, 192056400]$	$y^2=x^3-629100x+192056400$	3.4.0.a.1, 24.8.0-3.a.1.3, 156.8.0.?, 312.16.0.?	$[(570, 4320)]$
187200.fp1	187200pr1	187200.fp	187200pr	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{19} \cdot 3^{3} \cdot 5^{10} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$		$0$	$2488320$	$2.154274$	$-8538302475/26$	$0.97351$	$4.50865$	$[0, 0, 0, -1747500, 889150000]$	$y^2=x^3-1747500x+889150000$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 390.8.0.?, 1560.16.0.?	$[ ]$
187200.kz1	187200oq2	187200.kz	187200oq	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{19} \cdot 3^{9} \cdot 5^{4} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1$	$1$		$0$	$1492992$	$1.898861$	$-8538302475/26$	$0.97351$	$4.25618$	$[0, 0, 0, -629100, -192056400]$	$y^2=x^3-629100x-192056400$	3.4.0.a.1, 24.8.0-3.a.1.1, 78.8.0.?, 312.16.0.?	$[ ]$
187200.lb1	187200hs1	187200.lb	187200hs	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{19} \cdot 3^{3} \cdot 5^{10} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$12.00540094$	$1$		$0$	$2488320$	$2.154274$	$-8538302475/26$	$0.97351$	$4.50865$	$[0, 0, 0, -1747500, -889150000]$	$y^2=x^3-1747500x-889150000$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[(2054554/29, 2367362592/29)]$
187200.nc1	187200ot1	187200.nc	187200ot	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{19} \cdot 3^{3} \cdot 5^{4} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1$	$1$		$0$	$497664$	$1.349554$	$-8538302475/26$	$0.97351$	$3.71321$	$[0, 0, 0, -69900, 7113200]$	$y^2=x^3-69900x+7113200$	3.4.0.a.1, 24.8.0-3.a.1.2, 78.8.0.?, 312.16.0.?	$[ ]$
187200.ne1	187200if2	187200.ne	187200if	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{19} \cdot 3^{9} \cdot 5^{10} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$10.41447803$	$1$		$0$	$7464960$	$2.703579$	$-8538302475/26$	$0.97351$	$5.05162$	$[0, 0, 0, -15727500, 24007050000]$	$y^2=x^3-15727500x+24007050000$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[(3851196/41, 18993744/41)]$
286650.a1	286650a1	286650.a	286650a	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2 \cdot 3^{3} \cdot 5^{4} \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$5.396979092$	$1$		$2$	$933120$	$1.282789$	$-8538302475/26$	$0.97351$	$3.52354$	$[1, -1, 0, -53517, -4751909]$	$y^2+xy=x^3-x^2-53517x-4751909$	3.4.0.a.1, 21.8.0-3.a.1.1, 312.8.0.?, 2184.16.0.?	$[(2543, 126398)]$
286650.ij1	286650ij2	286650.ij	286650ij	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2 \cdot 3^{9} \cdot 5^{10} \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10920$	$16$	$0$	$6.474114232$	$1$		$0$	$13996800$	$2.636814$	$-8538302475/26$	$0.97351$	$4.81658$	$[1, -1, 0, -12041367, 16085858291]$	$y^2+xy=x^3-x^2-12041367x+16085858291$	3.4.0.a.1, 105.8.0.?, 312.8.0.?, 10920.16.0.?	$[(242995/11, -794704/11)]$
286650.iz1	286650iz1	286650.iz	286650iz	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2 \cdot 3^{3} \cdot 5^{10} \cdot 7^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10920$	$16$	$0$	$1$	$9$	$3$	$0$	$4665600$	$2.087509$	$-8538302475/26$	$0.97351$	$4.29201$	$[1, -1, 1, -1337930, -595326553]$	$y^2+xy+y=x^3-x^2-1337930x-595326553$	3.4.0.a.1, 105.8.0.?, 312.8.0.?, 10920.16.0.?	$[ ]$
286650.rk1	286650rk2	286650.rk	286650rk	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2 \cdot 3^{9} \cdot 5^{4} \cdot 7^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$1$	$1$		$0$	$2799360$	$1.832094$	$-8538302475/26$	$0.97351$	$4.04810$	$[1, -1, 1, -481655, 128783197]$	$y^2+xy+y=x^3-x^2-481655x+128783197$	3.4.0.a.1, 21.8.0-3.a.1.2, 312.8.0.?, 2184.16.0.?	$[ ]$

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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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