LMFDB - Elliptic curves over $\Q$ of conductor 8281

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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 (20 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Potentially good	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
8281.a1	8281m1	8281.a	8281m	$1$	$1$	$ 7^{2} \cdot 13^{2} $	$ - 7^{3} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$3$	9.9.0.1	3Nn	$1638$	$36$	$3$	$1.259732188$	$1$	$4$	$19968$	$1.128557$	$-4096$	$0.71571$	$4.16684$	$[0, 1, 1, -5126, -170166]$	$y^2+y=x^3+x^2-5126x-170166$	3.3.0.a.1, 9.9.0.a.1, 39.6.0.b.1, 42.6.0.b.1, 117.18.0.?, $\ldots$	$[(394, 7689)]$
8281.b1	8281l1	8281.b	8281l	$1$	$1$	$ 7^{2} \cdot 13^{2} $	$ - 7^{9} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$3$	9.9.0.1	3Nn	$1638$	$36$	$3$	$2.889311790$	$1$	$0$	$139776$	$2.101513$	$-4096$	$0.71571$	$5.46099$	$[0, -1, 1, -251190, 57864484]$	$y^2+y=x^3-x^2-251190x+57864484$	3.3.0.a.1, 9.9.0.a.1, 39.6.0.b.1, 42.6.0.b.1, 117.18.0.?, $\ldots$	$[(8293/6, 753463/6)]$
8281.c1	8281c1	8281.c	8281c	$1$	$1$	$ 7^{2} \cdot 13^{2} $	$ 7^{8} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2$	2.2.0.1	2Cn	$364$	$12$	$0$	$0.305399437$	$1$	$6$	$5544$	$0.422472$	$2457$	$0.71571$	$3.15947$	$[1, -1, 1, -279, -906]$	$y^2+xy+y=x^3-x^2-279x-906$	2.2.0.a.1, 52.4.0-2.a.1.1, 182.6.0.?, 364.12.0.?	$[(-12, 30)]$
8281.d1	8281g4	8281.d	8281g	$4$	$14$	$ 7^{2} \cdot 13^{2} $	$ 7^{9} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-28$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$0$	$32928$	$1.802864$	$16581375$	$1.19804$	$5.48972$	$[1, -1, 1, -307950, 65849606]$	$y^2+xy+y=x^3-x^2-307950x+65849606$		$[]$
8281.d2	8281g3	8281.d	8281g	$4$	$14$	$ 7^{2} \cdot 13^{2} $	$ - 7^{9} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-7$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$16464$	$1.456291$	$-3375$	$0.98030$	$4.59341$	$[1, -1, 1, -18115, 1158434]$	$y^2+xy+y=x^3-x^2-18115x+1158434$		$[]$
8281.d3	8281g2	8281.d	8281g	$4$	$14$	$ 7^{2} \cdot 13^{2} $	$ 7^{3} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-28$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$0$	$4704$	$0.829910$	$16581375$	$1.19804$	$4.19557$	$[1, -1, 1, -6285, -190186]$	$y^2+xy+y=x^3-x^2-6285x-190186$		$[]$
8281.d4	8281g1	8281.d	8281g	$4$	$14$	$ 7^{2} \cdot 13^{2} $	$ - 7^{3} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-7$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$2352$	$0.483336$	$-3375$	$0.98030$	$3.29926$	$[1, -1, 1, -370, -3272]$	$y^2+xy+y=x^3-x^2-370x-3272$		$[]$
8281.e1	8281f1	8281.e	8281f	$2$	$7$	$ 7^{2} \cdot 13^{2} $	$ - 7^{10} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$7$	7.24.0.3	7B.6.2	$364$	$96$	$2$	$1$	$1$	$0$	$70560$	$2.109386$	$-56723625/13$	$1.28311$	$5.84178$	$[1, -1, 1, -887620, -321717756]$	$y^2+xy+y=x^3-x^2-887620x-321717756$	7.24.0.b.1, 28.48.0-7.b.1.4, 52.2.0.a.1, 91.48.0.?, 364.96.2.?	$[]$
8281.e2	8281f2	8281.e	8281f	$2$	$7$	$ 7^{2} \cdot 13^{2} $	$ - 7^{10} \cdot 13^{13} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$7$	7.24.0.3	7B.6.2	$364$	$96$	$2$	$1$	$1$	$0$	$493920$	$3.082340$	$11397810375/62748517$	$1.05408$	$6.66692$	$[1, -1, 1, 5198915, 13311309106]$	$y^2+xy+y=x^3-x^2+5198915x+13311309106$	7.24.0.b.1, 28.48.0-7.b.1.3, 52.2.0.a.1, 91.48.0.?, 364.96.2.?	$[]$
8281.f1	8281b1	8281.f	8281b	$2$	$7$	$ 7^{2} \cdot 13^{2} $	$ - 7^{4} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$7$	7.24.0.3	7B.6.2	$364$	$96$	$2$	$0.446240310$	$1$	$4$	$10080$	$1.136431$	$-56723625/13$	$1.28311$	$4.54763$	$[1, -1, 1, -18115, 943128]$	$y^2+xy+y=x^3-x^2-18115x+943128$	7.24.0.b.1, 28.48.0-7.b.1.3, 52.2.0.a.1, 91.48.0.?, 364.96.2.?	$[(114, 534)]$
8281.f2	8281b2	8281.f	8281b	$2$	$7$	$ 7^{2} \cdot 13^{2} $	$ - 7^{4} \cdot 13^{13} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$7$	7.24.0.3	7B.6.2	$364$	$96$	$2$	$3.123682171$	$1$	$2$	$70560$	$2.109386$	$11397810375/62748517$	$1.05408$	$5.37277$	$[1, -1, 1, 106100, -38838796]$	$y^2+xy+y=x^3-x^2+106100x-38838796$	7.24.0.b.1, 28.48.0-7.b.1.4, 52.2.0.a.1, 91.48.0.?, 364.96.2.?	$[(842, 25013)]$
8281.g1	8281h1	8281.g	8281h	$1$	$1$	$ 7^{2} \cdot 13^{2} $	$ 7^{2} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2$	2.2.0.1	2Cn	$364$	$12$	$0$	$1$	$1$	$0$	$792$	$-0.550483$	$2457$	$0.71571$	$1.86532$	$[1, -1, 1, -6, 4]$	$y^2+xy+y=x^3-x^2-6x+4$	2.2.0.a.1, 182.6.0.?, 364.12.0.?	$[]$
8281.h1	8281d3	8281.h	8281d	$3$	$9$	$ 7^{2} \cdot 13^{2} $	$ - 7^{15} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$1638$	$144$	$3$	$1$	$1$	$0$	$290304$	$2.615532$	$-178643795968/524596891$	$1.15023$	$6.07178$	$[0, -1, 1, -971637, 908886292]$	$y^2+y=x^3-x^2-971637x+908886292$	3.4.0.a.1, 6.8.0-3.a.1.2, 9.12.0.a.1, 18.24.0-9.a.1.2, 117.36.0.?, $\ldots$	$[]$
8281.h2	8281d1	8281.h	8281d	$3$	$9$	$ 7^{2} \cdot 13^{2} $	$ - 7^{7} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$1638$	$144$	$3$	$1$	$1$	$0$	$32256$	$1.516922$	$-43614208/91$	$0.87141$	$4.95024$	$[0, -1, 1, -60727, -5750158]$	$y^2+y=x^3-x^2-60727x-5750158$	3.4.0.a.1, 6.8.0-3.a.1.1, 9.12.0.a.1, 18.24.0-9.a.1.1, 117.36.0.?, $\ldots$	$[]$
8281.h3	8281d2	8281.h	8281d	$3$	$9$	$ 7^{2} \cdot 13^{2} $	$ - 7^{9} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	3.12.0.1	3Cs	$1638$	$144$	$3$	$1$	$1$	$0$	$96768$	$2.066227$	$224755712/753571$	$0.95798$	$5.30531$	$[0, -1, 1, 104893, -28663685]$	$y^2+y=x^3-x^2+104893x-28663685$	3.12.0.a.1, 6.24.0-3.a.1.1, 117.36.0.?, 182.2.0.?, 234.72.0.?, $\ldots$	$[]$
8281.i1	8281a1	8281.i	8281a	$1$	$1$	$ 7^{2} \cdot 13^{2} $	$ 7^{8} \cdot 13^{8} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2$	4.4.0.2	2Cn	$364$	$12$	$0$	$10.29755530$	$1$	$0$	$72072$	$1.704947$	$2457$	$0.71571$	$4.86532$	$[1, -1, 0, -47098, -2131193]$	$y^2+xy=x^3-x^2-47098x-2131193$	2.2.0.a.1, 4.4.0-2.a.1.1, 182.6.0.?, 364.12.0.?	$[(-22758/11, 414193/11)]$
8281.j1	8281e1	8281.j	8281e	$1$	$1$	$ 7^{2} \cdot 13^{2} $	$ 7^{2} \cdot 13^{8} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2$	2.2.0.1	2Cn	$364$	$12$	$0$	$1$	$1$	$0$	$10296$	$0.731992$	$2457$	$0.71571$	$3.57117$	$[1, -1, 0, -961, 6488]$	$y^2+xy=x^3-x^2-961x+6488$	2.2.0.a.1, 28.4.0-2.a.1.1, 182.6.0.?, 364.12.0.?	$[]$
8281.k1	8281k1	8281.k	8281k	$1$	$1$	$ 7^{2} \cdot 13^{2} $	$ - 7^{3} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$3$	9.9.0.1	3Nn	$1638$	$36$	$3$	$1.518823837$	$1$	$0$	$1536$	$-0.153918$	$-4096$	$0.71571$	$2.46099$	$[0, 1, 1, -30, -87]$	$y^2+y=x^3+x^2-30x-87$	3.3.0.a.1, 9.9.0.a.1, 39.6.0.b.1, 42.6.0.b.1, 117.18.0.?, $\ldots$	$[(29/2, 87/2)]$
8281.l1	8281i1	8281.l	8281i	$1$	$1$	$ 7^{2} \cdot 13^{2} $	$ - 7^{7} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$					$182$	$2$	$0$	$1$	$1$	$0$	$32256$	$1.319099$	$110592/91$	$0.71571$	$4.28729$	$[0, 0, 1, 8281, -188393]$	$y^2+y=x^3+8281x-188393$	182.2.0.?	$[]$
8281.m1	8281j1	8281.m	8281j	$1$	$1$	$ 7^{2} \cdot 13^{2} $	$ - 7^{9} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$3$	9.9.0.1	3Nn	$1638$	$36$	$3$	$2.501671488$	$1$	$0$	$10752$	$0.819037$	$-4096$	$0.71571$	$3.75514$	$[0, -1, 1, -1486, 26795]$	$y^2+y=x^3-x^2-1486x+26795$	3.3.0.a.1, 9.9.0.a.1, 39.6.0.b.1, 42.6.0.b.1, 117.18.0.?, $\ldots$	$[(-207/4, 13345/4)]$

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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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