LMFDB - Elliptic curves over $\Q$ of conductor 46818

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

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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 (22 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
46818.a1	46818g1	46818.a	46818g	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{2} \cdot 3^{10} \cdot 17^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.4.0.1		$68$	$8$	$0$	$0.350111757$	$1$		$20$	$39168$	$0.425252$	$3087/4$	$0.81217$	$2.57904$	$1$	$[1, -1, 0, 201, 1169]$	$y^2+xy=x^3-x^2+201x+1169$	4.4.0.a.1, 68.8.0.b.1	$[(13, 70), (-4, 19)]$	$1$
46818.b1	46818a1	46818.b	46818a	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{7} \cdot 3^{10} \cdot 17^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$3.013918303$	$1$		$2$	$1451520$	$2.601845$	$-40945863537/181741696$	$1.00666$	$5.07538$	$1$	$[1, -1, 0, -808098, 823488020]$	$y^2+xy=x^3-x^2-808098x+823488020$	136.2.0.?	$[(-89, 29956)]$	$1$
46818.c1	46818b1	46818.c	46818b	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{5} \cdot 3^{4} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$4.191716298$	$1$		$2$	$69120$	$0.997159$	$934407/544$	$1.14595$	$3.26774$	$1$	$[1, -1, 0, 2547, -4475]$	$y^2+xy=x^3-x^2+2547x-4475$	136.2.0.?	$[(1101, 36008)]$	$1$
46818.d1	46818e3	46818.d	46818e	$4$	$21$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{7} \cdot 3^{6} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3, 7$	8.2.0.1, 3.4.0.1, 7.8.0.1	3B, 7B	$8568$	$768$	$21$	$1$	$1$		$0$	$211680$	$1.685974$	$-189613868625/128$	$1.12596$	$4.60843$	$1$	$[1, -1, 0, -311307, 66932549]$	$y^2+xy=x^3-x^2-311307x+66932549$	3.4.0.a.1, 7.8.0.a.1, 8.2.0.a.1, 21.64.1.a.4, 24.8.0.a.1, $\ldots$	$[ ]$	$1$
46818.d2	46818e4	46818.d	46818e	$4$	$21$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{21} \cdot 3^{10} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3, 7$	8.2.0.1, 3.4.0.1, 7.8.0.1	3B, 7B	$8568$	$768$	$21$	$1$	$1$		$0$	$635040$	$2.235279$	$-1159088625/2097152$	$1.11235$	$4.67488$	$1$	$[1, -1, 0, -246282, 95624180]$	$y^2+xy=x^3-x^2-246282x+95624180$	3.4.0.a.1, 7.8.0.a.1, 8.2.0.a.1, 21.64.1.a.1, 24.8.0.a.1, $\ldots$	$[ ]$	$1$
46818.d3	46818e2	46818.d	46818e	$4$	$21$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{3} \cdot 3^{10} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3, 7$	8.2.0.1, 3.4.0.1, 7.8.0.1	3B, 7B	$8568$	$768$	$21$	$1$	$1$		$0$	$90720$	$1.262325$	$-140625/8$	$1.17810$	$3.71331$	$1$	$[1, -1, 0, -12192, -539992]$	$y^2+xy=x^3-x^2-12192x-539992$	3.4.0.a.1, 7.8.0.a.1, 8.2.0.a.1, 21.64.1.a.3, 24.8.0.a.1, $\ldots$	$[ ]$	$1$
46818.d4	46818e1	46818.d	46818e	$4$	$21$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2 \cdot 3^{6} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3, 7$	8.2.0.1, 3.4.0.1, 7.8.0.1	3B, 7B	$8568$	$768$	$21$	$1$	$1$		$0$	$30240$	$0.713019$	$3375/2$	$1.42657$	$2.94914$	$1$	$[1, -1, 0, 813, -1585]$	$y^2+xy=x^3-x^2+813x-1585$	3.4.0.a.1, 7.8.0.a.1, 8.2.0.a.1, 21.64.1.a.2, 24.8.0.a.1, $\ldots$	$[ ]$	$1$
46818.e1	46818c1	46818.e	46818c	$2$	$3$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{2} \cdot 3^{6} \cdot 17^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.8.0.2, 3.4.0.1	3B	$204$	$128$	$1$	$3.059218834$	$1$		$2$	$60480$	$0.818800$	$-35937/4$	$1.00607$	$3.18545$	$1$	$[1, -1, 0, -1788, 32228]$	$y^2+xy=x^3-x^2-1788x+32228$	3.4.0.a.1, 4.8.0.b.1, 12.64.1.b.2, 51.8.0-3.a.1.2, 204.128.1.?	$[(26, 40)]$	$1$
46818.e2	46818c2	46818.e	46818c	$2$	$3$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{6} \cdot 3^{10} \cdot 17^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.8.0.2, 3.4.0.1	3B	$204$	$128$	$1$	$9.177656504$	$1$		$0$	$181440$	$1.368107$	$109503/64$	$1.28549$	$3.68133$	$1$	$[1, -1, 0, 11217, -48403]$	$y^2+xy=x^3-x^2+11217x-48403$	3.4.0.a.1, 4.8.0.b.1, 12.64.1.b.1, 51.8.0-3.a.1.1, 204.128.1.?	$[(14798/13, 2682285/13)]$	$1$
46818.f1	46818d1	46818.f	46818d	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{14} \cdot 3^{4} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$68$	$2$	$0$	$2.919984854$	$1$		$2$	$387072$	$1.712730$	$-132193123641/278528$	$0.97011$	$4.37091$	$1$	$[1, -1, 0, -132705, 18674173]$	$y^2+xy=x^3-x^2-132705x+18674173$	68.2.0.a.1	$[(114, 2183)]$	$1$
46818.g1	46818f1	46818.g	46818f	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{2} \cdot 3^{10} \cdot 17^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.4.0.1		$68$	$8$	$0$	$1$	$4$	$2$	$0$	$665856$	$1.841858$	$3087/4$	$0.81217$	$4.15978$	$1$	$[1, -1, 0, 58035, 5975513]$	$y^2+xy=x^3-x^2+58035x+5975513$	4.4.0.a.1, 68.8.0.b.1	$[ ]$	$1$
46818.h1	46818n1	46818.h	46818n	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{14} \cdot 3^{10} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$68$	$2$	$0$	$0.549505988$	$1$		$6$	$1161216$	$2.262035$	$-132193123641/278528$	$0.97011$	$4.98386$	$1$	$[1, -1, 1, -1194347, -503008325]$	$y^2+xy+y=x^3-x^2-1194347x-503008325$	68.2.0.a.1	$[(2155, 82154)]$	$1$
46818.i1	46818m1	46818.i	46818m	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{2} \cdot 3^{4} \cdot 17^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.4.0.1		$68$	$8$	$0$	$1$	$1$		$0$	$221952$	$1.292553$	$3087/4$	$0.81217$	$3.54683$	$1$	$[1, -1, 1, 6448, -223465]$	$y^2+xy+y=x^3-x^2+6448x-223465$	4.4.0.a.1, 68.8.0.b.1	$[ ]$	$1$
46818.j1	46818k2	46818.j	46818k	$2$	$3$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{2} \cdot 3^{12} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.8.0.2, 3.4.0.1	3B	$204$	$128$	$1$	$1$	$9$	$3$	$0$	$181440$	$1.368107$	$-35937/4$	$1.00607$	$3.79840$	$1$	$[1, -1, 1, -16094, -854063]$	$y^2+xy+y=x^3-x^2-16094x-854063$	3.4.0.a.1, 4.8.0.b.1, 12.64.1.b.2, 51.8.0-3.a.1.1, 68.16.0-4.b.1.1, $\ldots$	$[ ]$	$1$
46818.j2	46818k1	46818.j	46818k	$2$	$3$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{6} \cdot 3^{4} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.8.0.2, 3.4.0.1	3B	$204$	$128$	$1$	$1$	$1$		$0$	$60480$	$0.818800$	$109503/64$	$1.28549$	$3.06838$	$1$	$[1, -1, 1, 1246, 1377]$	$y^2+xy+y=x^3-x^2+1246x+1377$	3.4.0.a.1, 4.8.0.b.1, 12.64.1.b.1, 51.8.0-3.a.1.2, 68.16.0-4.b.1.1, $\ldots$	$[ ]$	$1$
46818.k1	46818h4	46818.k	46818h	$4$	$21$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{7} \cdot 3^{12} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3, 7$	8.2.0.1, 3.4.0.1, 7.8.0.1	3B, 7B	$8568$	$768$	$21$	$1$	$9$	$3$	$0$	$635040$	$2.235279$	$-189613868625/128$	$1.12596$	$5.22138$	$1$	$[1, -1, 1, -2801765, -1804377059]$	$y^2+xy+y=x^3-x^2-2801765x-1804377059$	3.4.0.a.1, 7.8.0.a.1, 8.2.0.a.1, 21.64.1.a.4, 24.8.0.a.1, $\ldots$	$[ ]$	$1$
46818.k2	46818h3	46818.k	46818h	$4$	$21$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{21} \cdot 3^{4} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3, 7$	8.2.0.1, 3.4.0.1, 7.8.0.1	3B, 7B	$8568$	$768$	$21$	$1$	$1$		$0$	$211680$	$1.685974$	$-1159088625/2097152$	$1.11235$	$4.06193$	$1$	$[1, -1, 1, -27365, -3532515]$	$y^2+xy+y=x^3-x^2-27365x-3532515$	3.4.0.a.1, 7.8.0.a.1, 8.2.0.a.1, 21.64.1.a.1, 24.8.0.a.1, $\ldots$	$[ ]$	$1$
46818.k3	46818h1	46818.k	46818h	$4$	$21$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{3} \cdot 3^{4} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3, 7$	8.2.0.1, 3.4.0.1, 7.8.0.1	3B, 7B	$8568$	$768$	$21$	$1$	$1$		$0$	$30240$	$0.713019$	$-140625/8$	$1.17810$	$3.10036$	$1$	$[1, -1, 1, -1355, 20451]$	$y^2+xy+y=x^3-x^2-1355x+20451$	3.4.0.a.1, 7.8.0.a.1, 8.2.0.a.1, 21.64.1.a.3, 24.8.0.a.1, $\ldots$	$[ ]$	$1$
46818.k4	46818h2	46818.k	46818h	$4$	$21$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2 \cdot 3^{12} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3, 7$	8.2.0.1, 3.4.0.1, 7.8.0.1	3B, 7B	$8568$	$768$	$21$	$1$	$9$	$3$	$0$	$90720$	$1.262325$	$3375/2$	$1.42657$	$3.56209$	$1$	$[1, -1, 1, 7315, 35479]$	$y^2+xy+y=x^3-x^2+7315x+35479$	3.4.0.a.1, 7.8.0.a.1, 8.2.0.a.1, 21.64.1.a.2, 24.8.0.a.1, $\ldots$	$[ ]$	$1$
46818.l1	46818i1	46818.l	46818i	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{7} \cdot 3^{4} \cdot 17^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$1$	$1$		$0$	$483840$	$2.052540$	$-40945863537/181741696$	$1.00666$	$4.46243$	$1$	$[1, -1, 1, -89789, -30469627]$	$y^2+xy+y=x^3-x^2-89789x-30469627$	136.2.0.?	$[ ]$	$1$
46818.m1	46818j1	46818.m	46818j	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{5} \cdot 3^{10} \cdot 17^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$136$	$2$	$0$	$1$	$1$		$0$	$207360$	$1.546465$	$934407/544$	$1.14595$	$3.88069$	$1$	$[1, -1, 1, 22921, 97903]$	$y^2+xy+y=x^3-x^2+22921x+97903$	136.2.0.?	$[ ]$	$1$
46818.n1	46818l1	46818.n	46818l	$1$	$1$	$ 2 \cdot 3^{4} \cdot 17^{2} $	$ - 2^{2} \cdot 3^{4} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.4.0.1		$68$	$8$	$0$	$1$	$1$		$0$	$13056$	$-0.124054$	$3087/4$	$0.81217$	$1.96609$	$1$	$[1, -1, 1, 22, -51]$	$y^2+xy+y=x^3-x^2+22x-51$	4.4.0.a.1, 68.8.0.b.1	$[ ]$	$1$

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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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