Elliptic curves over $\Q$ of conductor 20622

Results (17 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	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
20622.a1	20622a1	20622.a	20622a	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{6} \cdot 3 \cdot 7^{3} \cdot 491 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20622$	$2$	$0$	$0.344142708$	$1$		$16$	$7200$	$0.187878$	$-408023180713/32335296$	$0.83226$	$2.70411$	$[1, 1, 0, -154, 724]$	\(y^2+xy=x^3+x^2-154x+724\)	20622.2.0.?	$[(12, 22), (-9, 43)]$
20622.b1	20622d4	20622.b	20622d	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( 2^{5} \cdot 3^{4} \cdot 7^{4} \cdot 491 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.8	2B	$82488$	$48$	$0$	$1.179117940$	$1$		$6$	$72960$	$1.298462$	$65096426281618821097/3055685472$	$0.95140$	$4.59250$	$[1, 1, 0, -83806, 9303316]$	\(y^2+xy=x^3+x^2-83806x+9303316\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 168.24.0.?, 1964.12.0.?, $\ldots$	$[(151, 271)]$
20622.b2	20622d3	20622.b	20622d	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( 2^{5} \cdot 3 \cdot 7 \cdot 491^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$82488$	$48$	$0$	$4.716471763$	$1$		$2$	$72960$	$1.298462$	$70502835713233897/39056672632992$	$0.95350$	$3.90517$	$[1, 1, 0, -8606, -67116]$	\(y^2+xy=x^3+x^2-8606x-67116\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 84.12.0.?, 168.24.0.?, $\ldots$	$[(-59, 519)]$
20622.b3	20622d2	20622.b	20622d	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( 2^{10} \cdot 3^{2} \cdot 7^{2} \cdot 491^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.1	2Cs	$82488$	$48$	$0$	$2.358235881$	$1$		$8$	$36480$	$0.951887$	$15971213575426537/108868322304$	$0.90956$	$3.75570$	$[1, 1, 0, -5246, 143220]$	\(y^2+xy=x^3+x^2-5246x+143220\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 1964.12.0.?, $\ldots$	$[(37, 20)]$
20622.b4	20622d1	20622.b	20622d	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{20} \cdot 3 \cdot 7 \cdot 491 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.12	2B	$82488$	$48$	$0$	$4.716471763$	$1$		$3$	$18240$	$0.605314$	$-223980311017/10811867136$	$0.90096$	$3.07733$	$[1, 1, 0, -126, 4980]$	\(y^2+xy=x^3+x^2-126x+4980\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 84.12.0.?, 168.24.0.?, $\ldots$	$[(101, 967)]$
20622.c1	20622c1	20622.c	20622c	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{6} \cdot 3 \cdot 7 \cdot 491 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20622$	$2$	$0$	$0.523965813$	$1$		$4$	$3264$	$-0.144240$	$-6321363049/659904$	$0.90708$	$2.28838$	$[1, 1, 0, -38, 84]$	\(y^2+xy=x^3+x^2-38x+84\)	20622.2.0.?	$[(4, 2)]$
20622.d1	20622b1	20622.d	20622b	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{2} \cdot 3^{7} \cdot 7 \cdot 491 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20622$	$2$	$0$	$3.271593396$	$1$		$2$	$7392$	$0.273282$	$-4844824797961/30066876$	$0.85237$	$2.94134$	$[1, 1, 0, -352, -2708]$	\(y^2+xy=x^3+x^2-352x-2708\)	20622.2.0.?	$[(26, 68)]$
20622.e1	20622e1	20622.e	20622e	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{2} \cdot 3^{13} \cdot 7 \cdot 491 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20622$	$2$	$0$	$4.760423514$	$1$		$2$	$25792$	$0.741791$	$-393397793197417/21918752604$	$0.88713$	$3.39213$	$[1, 1, 0, -1526, -24672]$	\(y^2+xy=x^3+x^2-1526x-24672\)	20622.2.0.?	$[(142, 1556)]$
20622.f1	20622f1	20622.f	20622f	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{2} \cdot 3^{5} \cdot 7 \cdot 491 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20622$	$2$	$0$	$0.315020677$	$1$		$16$	$6560$	$-0.068798$	$30080231/3340764$	$0.83526$	$2.26202$	$[1, 0, 1, 6, 88]$	\(y^2+xy+y=x^3+6x+88\)	20622.2.0.?	$[(-1, 9), (-4, 3)]$
20622.g1	20622g2	20622.g	20622g	$2$	$3$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{6} \cdot 3^{3} \cdot 7^{3} \cdot 491 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$20622$	$16$	$0$	$1$	$4$	$2$	$0$	$384480$	$2.070927$	$-11965154517066396490542937/291017664$	$0.99466$	$5.81270$	$[1, 0, 1, -4765022, -4003948528]$	\(y^2+xy+y=x^3-4765022x-4003948528\)	3.8.0-3.a.1.1, 20622.16.0.?	$[]$
20622.g2	20622g1	20622.g	20622g	$2$	$3$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{2} \cdot 3^{9} \cdot 7 \cdot 491^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$20622$	$16$	$0$	$1$	$4$	$2$	$2$	$128160$	$1.521620$	$-22467615674643124777/65236972796604$	$0.94678$	$4.48592$	$[1, 0, 1, -58787, -5504758]$	\(y^2+xy+y=x^3-58787x-5504758\)	3.8.0-3.a.1.2, 20622.16.0.?	$[]$
20622.h1	20622j2	20622.h	20622j	$2$	$3$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{10} \cdot 3 \cdot 7^{3} \cdot 491^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$20622$	$16$	$0$	$1$	$1$		$0$	$377280$	$1.918821$	$-32619347021764199611153/124726807919616$	$0.97564$	$5.21830$	$[1, 0, 0, -665657, -209093511]$	\(y^2+xy=x^3-665657x-209093511\)	3.8.0-3.a.1.1, 20622.16.0.?	$[]$
20622.h2	20622j1	20622.h	20622j	$2$	$3$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{30} \cdot 3^{3} \cdot 7 \cdot 491 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$20622$	$16$	$0$	$1$	$1$		$2$	$125760$	$1.369514$	$-15344878361459473/99642167525376$	$0.94151$	$4.00365$	$[1, 0, 0, -5177, -501639]$	\(y^2+xy=x^3-5177x-501639\)	3.8.0-3.a.1.2, 20622.16.0.?	$[]$
20622.i1	20622h1	20622.i	20622h	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{18} \cdot 3 \cdot 7 \cdot 491 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20622$	$2$	$0$	$0.591681235$	$1$		$2$	$10656$	$0.499078$	$4501115240831/2702966784$	$0.89556$	$2.93286$	$[1, 0, 0, 344, -448]$	\(y^2+xy=x^3+344x-448\)	20622.2.0.?	$[(16, 88)]$
20622.j1	20622k2	20622.j	20622k	$2$	$7$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{2} \cdot 3 \cdot 7 \cdot 491^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$20622$	$96$	$2$	$13.04736995$	$1$		$0$	$998816$	$2.759453$	$-17959412105181401119111729/577896056532732884604$	$0.99631$	$5.85903$	$[1, 0, 0, -5455771, -5039899603]$	\(y^2+xy=x^3-5455771x-5039899603\)	7.48.0-7.a.2.2, 20622.96.2.?	$[(328219/10, 109777927/10)]$
20622.j2	20622k1	20622.j	20622k	$2$	$7$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{14} \cdot 3^{7} \cdot 7^{7} \cdot 491 \)	$1$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$20622$	$96$	$2$	$1.863909993$	$1$		$16$	$142688$	$1.786497$	$-3730574781442415089/14488936015970304$	$0.96168$	$4.51029$	$[1, 0, 0, -32311, 6205097]$	\(y^2+xy=x^3-32311x+6205097\)	7.48.0-7.a.1.2, 20622.96.2.?	$[(2, 2477)]$
20622.k1	20622i1	20622.k	20622i	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 491 \)	\( - 2^{6} \cdot 3 \cdot 7 \cdot 491 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20622$	$2$	$0$	$1$	$1$		$0$	$3744$	$-0.204426$	$103823/659904$	$0.86135$	$2.09928$	$[1, 0, 0, 1, -39]$	\(y^2+xy=x^3+x-39\)	20622.2.0.?	$[]$