LMFDB - Elliptic curves over $\Q$ of conductor 5220

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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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
5220.a1	5220m1	5220.a	5220m	$1$	$1$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{7} \cdot 5^{2} \cdot 29 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$174$	$2$	$0$	$0.082493606$	$1$	$30$	$2688$	$0.235038$	$-192914176/2175$	$0.79677$	$3.32482$	$[0, 0, 0, -273, 1753]$	$y^2=x^3-273x+1753$	174.2.0.?	$[(-1, 45), (9, 5)]$
5220.b1	5220i1	5220.b	5220i	$1$	$1$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{11} \cdot 5^{4} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$174$	$2$	$0$	$1.156383348$	$1$	$2$	$3840$	$0.797692$	$-47659369216/4404375$	$0.87919$	$3.98350$	$[0, 0, 0, -1713, -29387]$	$y^2=x^3-1713x-29387$	174.2.0.?	$[(164, 2025)]$
5220.c1	5220g1	5220.c	5220g	$1$	$1$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{8} \cdot 3^{7} \cdot 5 \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$870$	$2$	$0$	$0.166639136$	$1$	$8$	$960$	$0.201076$	$-65536/435$	$0.82245$	$3.00815$	$[0, 0, 0, -48, 452]$	$y^2=x^3-48x+452$	870.2.0.?	$[(4, 18)]$
5220.d1	5220b1	5220.d	5220b	$1$	$1$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{3} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$870$	$2$	$0$	$3.907429134$	$1$	$2$	$1440$	$0.393965$	$-11203633152/3625$	$0.97881$	$3.73600$	$[0, 0, 0, -888, -10188]$	$y^2=x^3-888x-10188$	870.2.0.?	$[(69, 507)]$
5220.e1	5220l1	5220.e	5220l	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ 2^{4} \cdot 3^{6} \cdot 5^{3} \cdot 29^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$2304$	$0.438494$	$226492416/105125$	$1.15496$	$3.34131$	$[0, 0, 0, -288, 837]$	$y^2=x^3-288x+837$	2.3.0.a.1, 10.6.0.a.1, 116.6.0.?, 580.12.0.?	$[ ]$
5220.e2	5220l2	5220.e	5220l	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{8} \cdot 3^{6} \cdot 5^{6} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$4608$	$0.785068$	$623331504/453125$	$1.02485$	$3.78347$	$[0, 0, 0, 1017, 6318]$	$y^2=x^3+1017x+6318$	2.3.0.a.1, 20.6.0.c.1, 116.6.0.?, 580.12.0.?	$[ ]$
5220.f1	5220a2	5220.f	5220a	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{9} \cdot 5^{6} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$174$	$16$	$0$	$2.310185007$	$1$	$0$	$3456$	$0.853263$	$-1419579648/453125$	$0.83797$	$3.99205$	$[0, 0, 0, -1593, -30483]$	$y^2=x^3-1593x-30483$	3.8.0-3.a.1.1, 174.16.0.?	$[(489/2, 10125/2)]$
5220.f2	5220a1	5220.f	5220a	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{3} \cdot 5^{2} \cdot 29^{3} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$174$	$16$	$0$	$0.770061669$	$1$	$8$	$1152$	$0.303957$	$813189888/609725$	$0.98400$	$3.10562$	$[0, 0, 0, 147, 373]$	$y^2=x^3+147x+373$	3.8.0-3.a.1.2, 174.16.0.?	$[(-1, 15)]$
5220.g1	5220k1	5220.g	5220k	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ 2^{4} \cdot 3^{10} \cdot 5^{5} \cdot 29^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$30720$	$1.851295$	$4150455958484156416/212878125$	$1.06098$	$6.10192$	$[0, 0, 0, -759288, 254658337]$	$y^2=x^3-759288x+254658337$	2.3.0.a.1, 10.6.0.a.1, 116.6.0.?, 580.12.0.?	$[ ]$
5220.g2	5220k2	5220.g	5220k	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{8} \cdot 3^{14} \cdot 5^{10} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$61440$	$2.197868$	$-258068272529292496/1858095703125$	$0.98568$	$6.10277$	$[0, 0, 0, -757983, 255577318]$	$y^2=x^3-757983x+255577318$	2.3.0.a.1, 20.6.0.c.1, 116.6.0.?, 580.12.0.?	$[ ]$
5220.h1	5220j1	5220.h	5220j	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ 2^{4} \cdot 3^{10} \cdot 5 \cdot 29^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$3072$	$0.625067$	$13608288256/340605$	$0.95001$	$3.81977$	$[0, 0, 0, -1128, -14263]$	$y^2=x^3-1128x-14263$	2.3.0.a.1, 10.6.0.a.1, 116.6.0.?, 580.12.0.?	$[ ]$
5220.h2	5220j2	5220.h	5220j	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{8} \cdot 3^{14} \cdot 5^{2} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$6144$	$0.971641$	$3286064/4756725$	$0.96085$	$4.08472$	$[0, 0, 0, 177, -45322]$	$y^2=x^3+177x-45322$	2.3.0.a.1, 20.6.0.c.1, 116.6.0.?, 580.12.0.?	$[ ]$
5220.i1	5220h1	5220.i	5220h	$1$	$1$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{25} \cdot 5^{6} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$174$	$2$	$0$	$4.077175493$	$1$	$2$	$109440$	$2.438362$	$-74881286942075067136/526649727234375$	$1.01546$	$6.44126$	$[0, 0, 0, -1991433, 1088227757]$	$y^2=x^3-1991433x+1088227757$	174.2.0.?	$[(956, 7625)]$
5220.j1	5220c1	5220.j	5220c	$1$	$1$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{9} \cdot 5^{2} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$174$	$2$	$0$	$0.238261198$	$1$	$6$	$5760$	$1.016916$	$-5364759575808/725$	$0.97910$	$4.90301$	$[0, 0, 0, -24813, 1504413]$	$y^2=x^3-24813x+1504413$	174.2.0.?	$[(99, 135)]$
5220.k1	5220e1	5220.k	5220e	$1$	$1$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{3} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$870$	$2$	$0$	$0.178703988$	$1$	$8$	$4320$	$0.943271$	$-11203633152/3625$	$0.97881$	$4.50603$	$[0, 0, 0, -7992, 275076]$	$y^2=x^3-7992x+275076$	870.2.0.?	$[(72, 270)]$
5220.l1	5220p2	5220.l	5220p	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{9} \cdot 5^{6} \cdot 29^{3} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$174$	$16$	$0$	$0.338402501$	$1$	$16$	$10368$	$1.383238$	$-795070868224/10289109375$	$0.96855$	$4.66307$	$[0, 0, 0, -4377, 538729]$	$y^2=x^3-4377x+538729$	3.8.0-3.a.1.2, 174.16.0.?	$[(53, 675)]$
5220.l2	5220p1	5220.l	5220p	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{15} \cdot 5^{2} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$174$	$16$	$0$	$1.015207505$	$1$	$2$	$3456$	$0.833931$	$1068359936/14270175$	$0.91051$	$3.88404$	$[0, 0, 0, 483, -19199]$	$y^2=x^3+483x-19199$	3.8.0-3.a.1.1, 174.16.0.?	$[(80, 729)]$
5220.m1	5220d1	5220.m	5220d	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{3} \cdot 5^{6} \cdot 29 $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$174$	$16$	$0$	$0.602945988$	$1$	$10$	$1152$	$0.303957$	$-1419579648/453125$	$0.83797$	$3.22202$	$[0, 0, 0, -177, 1129]$	$y^2=x^3-177x+1129$	3.8.0-3.a.1.2, 174.16.0.?	$[(8, 15)]$
5220.m2	5220d2	5220.m	5220d	$2$	$3$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{9} \cdot 5^{2} \cdot 29^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$174$	$16$	$0$	$1.808837965$	$1$	$2$	$3456$	$0.853263$	$813189888/609725$	$0.98400$	$3.87565$	$[0, 0, 0, 1323, -10071]$	$y^2=x^3+1323x-10071$	3.8.0-3.a.1.1, 174.16.0.?	$[(48, 405)]$
5220.n1	5220n1	5220.n	5220n	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$768$	$0.044658$	$3538944/725$	$0.87494$	$2.85548$	$[0, 0, 0, -72, 189]$	$y^2=x^3-72x+189$	2.3.0.a.1, 20.6.0.b.1, 58.6.0.a.1, 580.12.0.?	$[ ]$
5220.n2	5220n2	5220.n	5220n	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{8} \cdot 3^{6} \cdot 5 \cdot 29^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$1536$	$0.391232$	$2122416/4205$	$0.84263$	$3.22305$	$[0, 0, 0, 153, 1134]$	$y^2=x^3+153x+1134$	2.3.0.a.1, 20.6.0.a.1, 116.6.0.?, 580.12.0.?	$[ ]$
5220.o1	5220o1	5220.o	5220o	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ 2^{4} \cdot 3^{10} \cdot 5^{6} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$9216$	$1.039831$	$2816075628544/36703125$	$1.02348$	$4.44270$	$[0, 0, 0, -6672, 207389]$	$y^2=x^3-6672x+207389$	2.3.0.a.1, 20.6.0.b.1, 58.6.0.a.1, 580.12.0.?	$[ ]$
5220.o2	5220o2	5220.o	5220o	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{8} \cdot 3^{14} \cdot 5^{3} \cdot 29^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$	$1$	$18432$	$1.386406$	$-680136784/689725125$	$0.99577$	$4.66621$	$[0, 0, 0, -1047, 546014]$	$y^2=x^3-1047x+546014$	2.3.0.a.1, 20.6.0.a.1, 116.6.0.?, 580.12.0.?	$[ ]$
5220.p1	5220f1	5220.p	5220f	$1$	$1$	$ 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 $	$ - 2^{4} \cdot 3^{3} \cdot 5^{2} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$174$	$2$	$0$	$3.274031321$	$1$	$2$	$1920$	$0.467610$	$-5364759575808/725$	$0.97910$	$4.13297$	$[0, 0, 0, -2757, -55719]$	$y^2=x^3-2757x-55719$	174.2.0.?	$[(72, 345)]$

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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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