LMFDB - Elliptic curves over $\Q$ of conductor 33635

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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 (23 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
33635.a1	33635o1	33635.a	33635o	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{7} \cdot 7^{3} \cdot 31^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$6.798481160$	$1$	$2$	$2580480$	$2.900036$	$-4080168919667961856/25751796875$	$0.97614$	$6.08794$	$[0, 1, 1, -31992010, -69659326194]$	$y^2+y=x^3+x^2-31992010x-69659326194$	70.2.0.a.1	$[(435405, 287278937)]$
33635.b1	33635l1	33635.b	33635l	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5 \cdot 7 \cdot 31^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$140$	$2$	$0$	$0.913645005$	$1$	$4$	$2760$	$-0.363096$	$923521/35$	$0.87965$	$1.97671$	$[1, 0, 0, -20, -35]$	$y^2+xy=x^3-20x-35$	140.2.0.?	$[(-3, 2)]$
33635.c1	33635e2	33635.c	33635e	$2$	$2$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5^{8} \cdot 7^{2} \cdot 31^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.27	2B	$1736$	$48$	$1$	$12.61354071$	$1$	$0$	$1269760$	$2.786331$	$1693243664559/19140625$	$0.99344$	$5.66648$	$[1, -1, 1, -7397478, -7666289794]$	$y^2+xy+y=x^3-x^2-7397478x-7666289794$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 56.24.0.df.1, 124.12.0.?, $\ldots$	$[(17499265/39, 70594612798/39)]$
33635.c2	33635e1	33635.c	33635e	$2$	$2$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{4} \cdot 7^{4} \cdot 31^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.11	2B	$1736$	$48$	$1$	$6.306770359$	$1$	$3$	$634880$	$2.439758$	$-4019679/1500625$	$1.05167$	$5.04480$	$[1, -1, 1, -98683, -303265398]$	$y^2+xy+y=x^3-x^2-98683x-303265398$	2.3.0.a.1, 4.12.0.f.1, 56.24.0.dl.1, 62.6.0.b.1, 124.24.0.?, $\ldots$	$[(11368, 1205753)]$
33635.d1	33635d2	33635.d	33635d	$2$	$2$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5^{8} \cdot 7^{2} \cdot 31^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.27	2B	$1736$	$48$	$1$	$1.896279110$	$1$	$2$	$40960$	$1.069336$	$1693243664559/19140625$	$0.99344$	$3.68977$	$[1, -1, 1, -7698, 259322]$	$y^2+xy+y=x^3-x^2-7698x+259322$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 56.24.0.df.1, 124.12.0.?, $\ldots$	$[(-23, 662)]$
33635.d2	33635d1	33635.d	33635d	$2$	$2$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{4} \cdot 7^{4} \cdot 31^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.11	2B	$1736$	$48$	$1$	$0.948139555$	$1$	$3$	$20480$	$0.722763$	$-4019679/1500625$	$1.05167$	$3.06808$	$[1, -1, 1, -103, 10206]$	$y^2+xy+y=x^3-x^2-103x+10206$	2.3.0.a.1, 4.12.0.f.1, 56.24.0.dl.1, 62.6.0.b.1, 124.24.0.?, $\ldots$	$[(40, 242)]$
33635.e1	33635k4	33635.e	33635k	$4$	$4$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5 \cdot 7^{2} \cdot 31^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1240$	$48$	$0$	$5.346962956$	$1$	$0$	$368640$	$2.245777$	$258243633650241/226262645$	$0.93287$	$5.16043$	$[1, -1, 1, -1274947, 553996574]$	$y^2+xy+y=x^3-x^2-1274947x+553996574$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 10.6.0.a.1, 20.12.0.g.1, $\ldots$	$[(-3409/2, 259031/2)]$
33635.e2	33635k3	33635.e	33635k	$4$	$4$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5 \cdot 7^{8} \cdot 31^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$1240$	$48$	$0$	$21.38785182$	$1$	$0$	$368640$	$2.245777$	$74517479217441/893544155$	$1.00762$	$5.04119$	$[1, -1, 1, -842497, -294335786]$	$y^2+xy+y=x^3-x^2-842497x-294335786$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.z.1.5, 248.24.0.?, 620.24.0.?, $\ldots$	$[(74461245211/6270, 17024691768748531/6270)]$
33635.e3	33635k2	33635.e	33635k	$4$	$4$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5^{2} \cdot 7^{4} \cdot 31^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$620$	$48$	$0$	$10.69392591$	$1$	$2$	$184320$	$1.899204$	$116285729841/57684025$	$0.94207$	$4.42117$	$[1, -1, 1, -97722, 4467944]$	$y^2+xy+y=x^3-x^2-97722x+4467944$	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.3, 124.24.0.?, 620.48.0.?	$[(648107/19, 507722154/19)]$
33635.e4	33635k1	33635.e	33635k	$4$	$4$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{4} \cdot 7^{2} \cdot 31^{7} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$1240$	$48$	$0$	$5.346962956$	$1$	$5$	$92160$	$1.552631$	$1401168159/949375$	$0.89815$	$3.99724$	$[1, -1, 1, 22403, 527844]$	$y^2+xy+y=x^3-x^2+22403x+527844$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.13, 62.6.0.b.1, 124.24.0.?, $\ldots$	$[(1782, 74586)]$
33635.f1	33635f2	33635.f	33635f	$2$	$2$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5 \cdot 7 \cdot 31^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4340$	$12$	$0$	$22.01580289$	$1$	$0$	$153600$	$1.659613$	$711882749089/33635$	$0.86574$	$4.59499$	$[1, 1, 1, -178766, -29165432]$	$y^2+xy+y=x^3+x^2-178766x-29165432$	2.3.0.a.1, 124.6.0.?, 140.6.0.?, 4340.12.0.?	$[(2978720581/1647, 145731334172354/1647)]$
33635.f2	33635f1	33635.f	33635f	$2$	$2$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{2} \cdot 7^{2} \cdot 31^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4340$	$12$	$0$	$11.00790144$	$1$	$1$	$76800$	$1.313040$	$-148035889/37975$	$0.89182$	$3.81681$	$[1, 1, 1, -10591, -508412]$	$y^2+xy+y=x^3+x^2-10591x-508412$	2.3.0.a.1, 62.6.0.b.1, 140.6.0.?, 4340.12.0.?	$[(114256/27, 24204556/27)]$
33635.g1	33635h1	33635.g	33635h	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5 \cdot 7 \cdot 31^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$140$	$2$	$0$	$1$	$1$	$0$	$85560$	$1.353897$	$923521/35$	$0.87965$	$3.95343$	$[1, 1, 1, -19240, 984982]$	$y^2+xy+y=x^3+x^2-19240x+984982$	140.2.0.?	$[]$
33635.h1	33635j1	33635.h	33635j	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{3} \cdot 7 \cdot 31^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$1.476904050$	$1$	$4$	$1105920$	$2.235863$	$-63693291257856/808080875$	$1.11328$	$5.02822$	$[0, 0, 1, -799552, 278180910]$	$y^2+y=x^3-799552x+278180910$	70.2.0.a.1	$[(558, 2402)]$
33635.i1	33635c1	33635.i	33635c	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5 \cdot 7^{4} \cdot 31^{13} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$310$	$2$	$0$	$2.476350252$	$1$	$0$	$3225600$	$3.188530$	$235131885842333696/330288932402555$	$1.05942$	$5.84829$	$[0, -1, 1, 12357179, -19979133239]$	$y^2+y=x^3-x^2+12357179x-19979133239$	310.2.0.?	$[(630295/3, 501010129/3)]$
33635.j1	33635b3	33635.j	33635b	$3$	$9$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{9} \cdot 7 \cdot 31^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$19530$	$144$	$3$	$3.646636440$	$1$	$0$	$181440$	$1.844456$	$-250523582464/13671875$	$1.02112$	$4.50344$	$[0, -1, 1, -126211, 18095692]$	$y^2+y=x^3-x^2-126211x+18095692$	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.2, 70.2.0.a.1, 93.8.0.?, $\ldots$	$[(301/2, 24021/2)]$
33635.j2	33635b1	33635.j	33635b	$3$	$9$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5 \cdot 7 \cdot 31^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$19530$	$144$	$3$	$3.646636440$	$1$	$2$	$20160$	$0.745844$	$-262144/35$	$0.88715$	$3.19362$	$[0, -1, 1, -1281, -19158]$	$y^2+y=x^3-x^2-1281x-19158$	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.1, 70.2.0.a.1, 93.8.0.?, $\ldots$	$[(1168, 39881)]$
33635.j3	33635b2	33635.j	33635b	$3$	$9$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{3} \cdot 7^{3} \cdot 31^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$19530$	$144$	$3$	$1.215545480$	$1$	$4$	$60480$	$1.295149$	$71991296/42875$	$1.06493$	$3.71244$	$[0, -1, 1, 8329, 47151]$	$y^2+y=x^3-x^2+8329x+47151$	3.12.0.a.1, 63.36.0.b.1, 70.2.0.a.1, 93.24.0.?, 210.24.1.?, $\ldots$	$[(21, 480)]$
33635.k1	33635i1	33635.k	33635i	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5^{3} \cdot 7^{2} \cdot 31^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$10$	$2$	$0$	$0.256802745$	$1$	$4$	$4320$	$0.012112$	$27426816/6125$	$0.82489$	$2.30205$	$[0, 0, 1, -62, 147]$	$y^2+y=x^3-62x+147$	10.2.0.a.1	$[(-3, 17)]$
33635.l1	33635g1	33635.l	33635g	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ 5^{3} \cdot 7^{2} \cdot 31^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$10$	$2$	$0$	$1$	$1$	$0$	$133920$	$1.729105$	$27426816/6125$	$0.82489$	$4.27876$	$[0, 0, 1, -59582, -4386725]$	$y^2+y=x^3-59582x-4386725$	10.2.0.a.1	$[]$
33635.m1	33635a1	33635.m	33635a	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{3} \cdot 7^{4} \cdot 31^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$310$	$2$	$0$	$1$	$1$	$0$	$276480$	$1.733065$	$884736/9303875$	$1.05871$	$4.23133$	$[0, 0, 1, 1922, 4371829]$	$y^2+y=x^3+1922x+4371829$	310.2.0.?	$[]$
33635.n1	33635n1	33635.n	33635n	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5^{17} \cdot 7 \cdot 31^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$2.761369245$	$1$	$0$	$12533760$	$3.425446$	$-4334063657515831296/5132293701171875$	$1.02008$	$6.20060$	$[0, 0, 1, -32642287, 125285894097]$	$y^2+y=x^3-32642287x+125285894097$	70.2.0.a.1	$[(-208103/6, 75078017/6)]$
33635.o1	33635m1	33635.o	33635m	$1$	$1$	$ 5 \cdot 7 \cdot 31^{2} $	$ - 5 \cdot 7 \cdot 31^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$70$	$2$	$0$	$13.85373925$	$1$	$0$	$122880$	$1.264519$	$-4096/33635$	$0.87715$	$3.69192$	$[0, 1, 1, -320, 262771]$	$y^2+y=x^3+x^2-320x+262771$	70.2.0.a.1	$[(28789973/286, 154949246613/286)]$

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Elliptic curves over $\Q$
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Genus 2 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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