LMFDB - Elliptic curves over $\Q$ of conductor 3432

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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 (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
3432.a1	3432g5	3432.a	3432g	$6$	$8$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 3^{16} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.45	2B	$2288$	$192$	$1$	$1$	$4$	$2$	$1$	$12288$	$1.600821$	$29237205357427394/80023854339$	$0.98547$	$5.59383$	$[0, -1, 0, -81504, -8907732]$	$y^2=x^3-x^2-81504x-8907732$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.f.1.3, 88.48.0.?, $\ldots$	$[]$
3432.a2	3432g3	3432.a	3432g	$6$	$8$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{10} \cdot 3^{8} \cdot 11^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.31	2Cs	$1144$	$192$	$1$	$1$	$1$		$3$	$6144$	$1.254246$	$39383007958948/22674035241$	$1.15819$	$4.69676$	$[0, -1, 0, -7144, -14276]$	$y^2=x^3-x^2-7144x-14276$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.d.1.2, 88.96.0.?, 104.96.0.?, $\ldots$	$[]$
3432.a3	3432g2	3432.a	3432g	$6$	$8$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{8} \cdot 3^{4} \cdot 11^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.26	2Cs	$1144$	$192$	$1$	$1$	$1$		$7$	$3072$	$0.907673$	$45551779131472/200420649$	$1.04548$	$4.54434$	$[0, -1, 0, -4724, 126084]$	$y^2=x^3-x^2-4724x+126084$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.d.2.1, 52.48.0-52.c.1.1, 88.96.0.?, $\ldots$	$[]$
3432.a4	3432g1	3432.a	3432g	$6$	$8$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 13 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.30	2B	$2288$	$192$	$1$	$1$	$1$		$3$	$1536$	$0.561099$	$726516846671872/14157$	$0.98077$	$4.54395$	$[0, -1, 0, -4719, 126360]$	$y^2=x^3-x^2-4719x+126360$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.f.2.3, 26.6.0.b.1, $\ldots$	$[]$
3432.a5	3432g4	3432.a	3432g	$6$	$8$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{10} \cdot 3^{2} \cdot 11^{8} \cdot 13 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.160	2B	$2288$	$192$	$1$	$1$	$1$		$3$	$6144$	$1.254246$	$-1463944682308/25079989077$	$0.98022$	$4.71259$	$[0, -1, 0, -2384, 248700]$	$y^2=x^3-x^2-2384x+248700$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.ba.2.2, 52.24.0-52.h.1.2, 104.96.0.?, $\ldots$	$[]$
3432.a6	3432g6	3432.a	3432g	$6$	$8$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{11} \cdot 3^{4} \cdot 11 \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.175	2B	$2288$	$192$	$1$	$1$	$1$		$1$	$12288$	$1.600821$	$1249482637192606/726816072411$	$1.04802$	$5.20657$	$[0, -1, 0, 28496, -142580]$	$y^2=x^3-x^2+28496x-142580$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.1.1, 88.96.0.?, 208.96.0.?, $\ldots$	$[]$
3432.b1	3432a1	3432.b	3432a	$1$	$1$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{11} \cdot 3^{10} \cdot 11 \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1144$	$2$	$0$	$1.817928263$	$1$		$0$	$4800$	$1.111540$	$-6184708364018/1427037183$	$0.94194$	$4.59572$	$[0, -1, 0, -4856, -152436]$	$y^2=x^3-x^2-4856x-152436$	1144.2.0.?	$[(365/2, 3159/2)]$
3432.c1	3432f2	3432.c	3432f	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{10} \cdot 3^{3} \cdot 11^{2} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1716$	$12$	$0$	$1$	$1$		$1$	$1536$	$0.450849$	$15927506500/552123$	$0.87912$	$3.73703$	$[0, -1, 0, -528, -4356]$	$y^2=x^3-x^2-528x-4356$	2.3.0.a.1, 12.6.0.a.1, 572.6.0.?, 1716.12.0.?	$[]$
3432.c2	3432f1	3432.c	3432f	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 3^{6} \cdot 11 \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1716$	$12$	$0$	$1$	$1$		$1$	$768$	$0.104276$	$686000/104247$	$0.88116$	$3.01571$	$[0, -1, 0, 12, -252]$	$y^2=x^3-x^2+12x-252$	2.3.0.a.1, 12.6.0.b.1, 286.6.0.?, 1716.12.0.?	$[]$
3432.d1	3432b1	3432.d	3432b	$1$	$1$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{11} \cdot 3^{2} \cdot 11^{3} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1144$	$2$	$0$	$1$	$1$		$0$	$1728$	$0.320888$	$254527054/155727$	$0.89661$	$3.31407$	$[0, 1, 0, 168, -144]$	$y^2=x^3+x^2+168x-144$	1144.2.0.?	$[]$
3432.e1	3432d3	3432.e	3432d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 3 \cdot 11^{4} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3432$	$48$	$0$	$4.963961858$	$1$		$3$	$2048$	$0.624378$	$267335955794/570999$	$0.91164$	$4.16863$	$[0, 1, 0, -1704, -27600]$	$y^2=x^3+x^2-1704x-27600$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 52.12.0-4.c.1.1, 88.12.0.?, $\ldots$	$[(119, 1212)]$
3432.e2	3432d4	3432.e	3432d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 3 \cdot 11 \cdot 13^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3432$	$48$	$0$	$4.963961858$	$1$		$1$	$2048$	$0.624378$	$169556172914/942513$	$0.90779$	$4.11270$	$[0, 1, 0, -1464, 20976]$	$y^2=x^3+x^2-1464x+20976$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 44.12.0-4.c.1.1, 104.12.0.?, $\ldots$	$[(223/3, 620/3)]$
3432.e3	3432d2	3432.e	3432d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{10} \cdot 3^{2} \cdot 11^{2} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3432$	$48$	$0$	$2.481980929$	$1$		$7$	$1024$	$0.277805$	$324730948/184041$	$0.91099$	$3.25885$	$[0, 1, 0, -144, -144]$	$y^2=x^3+x^2-144x-144$	2.6.0.a.1, 24.12.0-2.a.1.1, 44.12.0-2.a.1.1, 52.12.0-2.a.1.1, 264.24.0.?, $\ldots$	$[(15, 36)]$
3432.e4	3432d1	3432.e	3432d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 3^{4} \cdot 11 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3432$	$48$	$0$	$1.240990464$	$1$		$5$	$512$	$-0.068769$	$19600688/11583$	$0.85042$	$2.74371$	$[0, 1, 0, 36, 0]$	$y^2=x^3+x^2+36x$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 44.12.0-4.c.1.2, 52.12.0-4.c.1.2, $\ldots$	$[(3, 12)]$
3432.f1	3432c2	3432.f	3432c	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{10} \cdot 3^{7} \cdot 11^{6} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1716$	$12$	$0$	$0.288541949$	$1$		$9$	$10752$	$1.584995$	$7382814913718500/654774260283$	$0.97740$	$5.33963$	$[0, 1, 0, -40888, -2941984]$	$y^2=x^3+x^2-40888x-2941984$	2.3.0.a.1, 12.6.0.a.1, 572.6.0.?, 1716.12.0.?	$[(-100, 396)]$
3432.f2	3432c1	3432.f	3432c	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 3^{14} \cdot 11^{3} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1716$	$12$	$0$	$0.577083899$	$1$		$9$	$5376$	$1.238420$	$10017976862000/82759712607$	$0.97191$	$4.67596$	$[0, 1, 0, 2852, -212608]$	$y^2=x^3+x^2+2852x-212608$	2.3.0.a.1, 12.6.0.b.1, 286.6.0.?, 1716.12.0.?	$[(71, 594)]$
3432.g1	3432h2	3432.g	3432h	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 3^{14} \cdot 11^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$18816$	$1.661879$	$5718957389087906/1075876263891$	$0.98270$	$5.39341$	$[0, 1, 0, -47312, 3238368]$	$y^2=x^3+x^2-47312x+3238368$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[]$
3432.g2	3432h1	3432.g	3432h	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{10} \cdot 3^{7} \cdot 11^{6} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$9408$	$1.315304$	$22494434350748/50367250791$	$0.96738$	$4.75743$	$[0, 1, 0, 5928, 299520]$	$y^2=x^3+x^2+5928x+299520$	2.3.0.a.1, 78.6.0.?, 88.6.0.?, 3432.12.0.?	$[]$
3432.h1	3432i2	3432.h	3432i	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 3^{6} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$1920$	$0.501667$	$2361864386/1355211$	$0.95919$	$3.58773$	$[0, 1, 0, -352, -352]$	$y^2=x^3+x^2-352x-352$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[]$
3432.h2	3432i1	3432.h	3432i	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{10} \cdot 3^{3} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$960$	$0.155093$	$72765788/42471$	$0.91365$	$3.07512$	$[0, 1, 0, 88, 0]$	$y^2=x^3+x^2+88x$	2.3.0.a.1, 78.6.0.?, 88.6.0.?, 3432.12.0.?	$[]$
3432.i1	3432e3	3432.i	3432e	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{10} \cdot 3^{3} \cdot 11^{2} \cdot 13^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$312$	$48$	$0$	$1$	$1$		$1$	$10752$	$1.344479$	$36652193922790372/93308787$	$0.98318$	$5.53646$	$[0, 1, 0, -69752, -7113888]$	$y^2=x^3+x^2-69752x-7113888$	2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 104.24.0.?, 312.48.0.?	$[]$
3432.i2	3432e2	3432.i	3432e	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{8} \cdot 3^{6} \cdot 11^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$156$	$48$	$0$	$1$	$1$		$3$	$5376$	$0.997906$	$37109806448848/1803785841$	$0.93543$	$4.51917$	$[0, 1, 0, -4412, -109440]$	$y^2=x^3+x^2-4412x-109440$	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 52.24.0-52.b.1.1, 156.48.0.?	$[]$
3432.i3	3432e1	3432.i	3432e	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{4} \cdot 3^{12} \cdot 11^{2} \cdot 13 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$312$	$48$	$0$	$1$	$1$		$3$	$2688$	$0.651332$	$3122884507648/835956693$	$0.95399$	$3.87456$	$[0, 1, 0, -767, 5742]$	$y^2=x^3+x^2-767x+5742$	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 26.6.0.b.1, 52.24.0-52.g.1.2, $\ldots$	$[]$
3432.i4	3432e4	3432.i	3432e	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 13 $	$ - 2^{10} \cdot 3^{3} \cdot 11^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$312$	$48$	$0$	$1$	$1$		$1$	$10752$	$1.344479$	$1915049403068/75239967231$	$0.99502$	$4.84164$	$[0, 1, 0, 2608, -418320]$	$y^2=x^3+x^2+2608x-418320$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$	$[]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$

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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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