LMFDB - Elliptic curves over $\Q$ of conductor 10647

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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

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Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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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
10647.a1	10647h1	10647.a	10647h	$1$	$1$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{6} \cdot 7 \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$0.308564554$	$1$	$6$	$21504$	$0.895452$	$110592/91$	$0.71571$	$3.62287$	$[0, 0, 1, 1521, -14830]$	$y^2+y=x^3+1521x-14830$	182.2.0.?	$[(78, 760)]$
10647.b1	10647i2	10647.b	10647i	$2$	$5$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{8} \cdot 7^{5} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$2730$	$48$	$1$	$1$	$1$	$0$	$1248000$	$3.034939$	$-13383627864961024/151263$	$1.15507$	$7.20466$	$[0, 0, 1, -97803849, -372290571468]$	$y^2+y=x^3-97803849x-372290571468$	5.6.0.a.1, 65.12.0.a.1, 70.12.0.a.1, 182.2.0.?, 195.24.0.?, $\ldots$	$[]$
10647.b2	10647i1	10647.b	10647i	$2$	$5$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{16} \cdot 7 \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$2730$	$48$	$1$	$1$	$1$	$0$	$249600$	$2.230221$	$5451776/413343$	$1.25184$	$5.39794$	$[0, 0, 1, 72501, -85675860]$	$y^2+y=x^3+72501x-85675860$	5.6.0.a.1, 65.12.0.a.2, 70.12.0.a.2, 182.2.0.?, 195.24.0.?, $\ldots$	$[]$
10647.c1	10647d1	10647.c	10647d	$1$	$1$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{10} \cdot 7^{3} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1$	$1$	$0$	$64512$	$1.623568$	$-2019487744/361179$	$0.90207$	$4.71009$	$[0, 0, 1, -40053, -3530030]$	$y^2+y=x^3-40053x-3530030$	182.2.0.?	$[]$
10647.d1	10647f5	10647.d	10647f	$6$	$8$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ 3^{7} \cdot 7^{2} \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$4368$	$192$	$1$	$0.548620843$	$1$	$10$	$73728$	$1.905987$	$53297461115137/147$	$1.05087$	$5.77894$	$[1, -1, 1, -1192496, 501523832]$	$y^2+xy+y=x^3-x^2-1192496x+501523832$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$	$[(504, 5071)]$
10647.d2	10647f4	10647.d	10647f	$6$	$8$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ 3^{8} \cdot 7^{4} \cdot 13^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.18	2Cs	$2184$	$192$	$1$	$1.097241687$	$1$	$12$	$36864$	$1.559412$	$13027640977/21609$	$1.08149$	$4.88208$	$[1, -1, 1, -74561, 7843736]$	$y^2+xy+y=x^3-x^2-74561x+7843736$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 24.48.0.j.2, $\ldots$	$[(36, 2263)]$
10647.d3	10647f3	10647.d	10647f	$6$	$8$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ 3^{14} \cdot 7 \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.88	2B	$4368$	$192$	$1$	$4.388966748$	$1$	$2$	$36864$	$1.559412$	$6570725617/45927$	$1.00160$	$4.80827$	$[1, -1, 1, -59351, -5516728]$	$y^2+xy+y=x^3-x^2-59351x-5516728$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 48.48.0.bf.1, $\ldots$	$[(907, 25741)]$
10647.d4	10647f6	10647.d	10647f	$6$	$8$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{7} \cdot 7^{8} \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.90	2B	$4368$	$192$	$1$	$0.548620843$	$1$	$8$	$73728$	$1.905987$	$-4354703137/17294403$	$1.04266$	$4.98629$	$[1, -1, 1, -51746, 12717020]$	$y^2+xy+y=x^3-x^2-51746x+12717020$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$	$[(-146, 4213)]$
10647.d5	10647f2	10647.d	10647f	$6$	$8$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ 3^{10} \cdot 7^{2} \cdot 13^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.10	2Cs	$2184$	$192$	$1$	$2.194483374$	$1$	$8$	$18432$	$1.212839$	$7189057/3969$	$1.14862$	$4.07304$	$[1, -1, 1, -6116, 41006]$	$y^2+xy+y=x^3-x^2-6116x+41006$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$	$[(0, 202)]$
10647.d6	10647f1	10647.d	10647f	$6$	$8$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{8} \cdot 7 \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.1	2B	$4368$	$192$	$1$	$4.388966748$	$1$	$3$	$9216$	$0.866265$	$103823/63$	$0.97868$	$3.61606$	$[1, -1, 1, 1489, 4502]$	$y^2+xy+y=x^3-x^2+1489x+4502$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$	$[(222, 3241)]$
10647.e1	10647b1	10647.e	10647b	$2$	$2$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ 3^{9} \cdot 7 \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1092$	$12$	$0$	$1$	$1$	$1$	$16128$	$1.196384$	$421875/91$	$0.93663$	$4.12267$	$[1, -1, 1, -7130, -181736]$	$y^2+xy+y=x^3-x^2-7130x-181736$	2.3.0.a.1, 12.6.0.c.1, 364.6.0.?, 546.6.0.?, 1092.12.0.?	$[]$
10647.e2	10647b2	10647.e	10647b	$2$	$2$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{9} \cdot 7^{2} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1092$	$12$	$0$	$1$	$1$	$0$	$32256$	$1.542957$	$4492125/8281$	$0.90809$	$4.46207$	$[1, -1, 1, 15685, -1121714]$	$y^2+xy+y=x^3-x^2+15685x-1121714$	2.3.0.a.1, 6.6.0.a.1, 364.6.0.?, 1092.12.0.?	$[]$
10647.f1	10647c3	10647.f	10647c	$3$	$9$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{6} \cdot 7^{9} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$1638$	$144$	$3$	$1$	$1$	$0$	$145152$	$2.191883$	$-178643795968/524596891$	$1.15023$	$5.35899$	$[0, 0, 1, -178464, 71519490]$	$y^2+y=x^3-178464x+71519490$	3.4.0.a.1, 9.12.0.a.1, 39.8.0-3.a.1.1, 42.8.0-3.a.1.2, 117.72.0.?, $\ldots$	$[]$
10647.f2	10647c1	10647.f	10647c	$3$	$9$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{6} \cdot 7 \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$1638$	$144$	$3$	$1$	$1$	$0$	$16128$	$1.093273$	$-43614208/91$	$0.87141$	$4.26784$	$[0, 0, 1, -11154, -454230]$	$y^2+y=x^3-11154x-454230$	3.4.0.a.1, 9.12.0.a.1, 39.8.0-3.a.1.2, 42.8.0-3.a.1.1, 117.72.0.?, $\ldots$	$[]$
10647.f3	10647c2	10647.f	10647c	$3$	$9$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{6} \cdot 7^{3} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$1638$	$144$	$3$	$1$	$1$	$0$	$48384$	$1.642578$	$224755712/753571$	$0.95798$	$4.61329$	$[0, 0, 1, 19266, -2253573]$	$y^2+y=x^3+19266x-2253573$	3.12.0.a.1, 39.24.0-3.a.1.1, 42.24.0-3.a.1.1, 117.72.0.?, 182.2.0.?, $\ldots$	$[]$
10647.g1	10647a1	10647.g	10647a	$2$	$2$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ 3^{3} \cdot 7 \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1092$	$12$	$0$	$1$	$1$	$1$	$5376$	$0.647078$	$421875/91$	$0.93663$	$3.41183$	$[1, -1, 0, -792, 6995]$	$y^2+xy=x^3-x^2-792x+6995$	2.3.0.a.1, 12.6.0.c.1, 364.6.0.?, 546.6.0.?, 1092.12.0.?	$[]$
10647.g2	10647a2	10647.g	10647a	$2$	$2$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{3} \cdot 7^{2} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1092$	$12$	$0$	$1$	$1$	$0$	$10752$	$0.993651$	$4492125/8281$	$0.90809$	$3.75122$	$[1, -1, 0, 1743, 40964]$	$y^2+xy=x^3-x^2+1743x+40964$	2.3.0.a.1, 6.6.0.a.1, 364.6.0.?, 1092.12.0.?	$[]$
10647.h1	10647g1	10647.h	10647g	$1$	$1$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{14} \cdot 7^{7} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$2.007875668$	$1$	$0$	$903168$	$3.022293$	$1811564780171264/11870974573731$	$1.04721$	$6.41093$	$[0, 0, 1, 3862833, 9388972323]$	$y^2+y=x^3+3862833x+9388972323$	182.2.0.?	$[(7241/4, 6782107/4)]$
10647.i1	10647e2	10647.i	10647e	$2$	$5$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{8} \cdot 7^{5} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$2730$	$48$	$1$	$29.01378152$	$1$	$0$	$96000$	$1.752464$	$-13383627864961024/151263$	$1.15507$	$5.54504$	$[0, 0, 1, -578721, -169454061]$	$y^2+y=x^3-578721x-169454061$	5.6.0.a.1, 65.12.0.a.1, 70.12.0.a.1, 182.2.0.?, 195.24.0.?, $\ldots$	$[(31837530375833/160232, 131369192877071924285/160232)]$
10647.i2	10647e1	10647.i	10647e	$2$	$5$	$ 3^{2} \cdot 7 \cdot 13^{2} $	$ - 3^{16} \cdot 7 \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$2730$	$48$	$1$	$5.802756305$	$1$	$0$	$19200$	$0.947745$	$5451776/413343$	$1.25184$	$3.73832$	$[0, 0, 1, 429, -38997]$	$y^2+y=x^3+429x-38997$	5.6.0.a.1, 65.12.0.a.2, 70.12.0.a.2, 182.2.0.?, 195.24.0.?, $\ldots$	$[(1937/8, 20921/8)]$

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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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