Elliptic curves over $\Q$ of conductor 14586

Results (22 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
14586.a1	14586c1	14586.a	14586c	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{6} \cdot 3 \cdot 11 \cdot 13^{3} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$29172$	$2$	$0$	$0.188236318$	$1$		$6$	$4896$	$0.199525$	$-15124197817/78881088$	$0.85038$	$2.68501$	$[1, 1, 0, -51, 429]$	\(y^2+xy=x^3+x^2-51x+429\)	29172.2.0.?	$[(14, 45)]$
14586.b1	14586a1	14586.b	14586a	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{22} \cdot 3^{7} \cdot 11^{5} \cdot 13 \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$29172$	$2$	$0$	$0.792295776$	$1$		$4$	$234080$	$2.114914$	$-5275941807135921123097/326485867713527808$	$0.97660$	$5.22737$	$[1, 1, 0, -362681, 88298661]$	\(y^2+xy=x^3+x^2-362681x+88298661\)	29172.2.0.?	$[(-110, 11319)]$
14586.c1	14586b1	14586.c	14586b	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( 2^{6} \cdot 3^{4} \cdot 11^{2} \cdot 13^{4} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.4	2B	$136$	$12$	$0$	$0.652198938$	$1$		$9$	$21504$	$0.939880$	$3047678972871625/304559880768$	$0.90943$	$3.71859$	$[1, 1, 0, -3020, -59376]$	\(y^2+xy=x^3+x^2-3020x-59376\)	2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.?	$[(-37, 77)]$
14586.c2	14586b2	14586.c	14586b	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{3} \cdot 3^{8} \cdot 11^{4} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$136$	$12$	$0$	$1.304397877$	$1$		$6$	$43008$	$1.286453$	$5783051584712375/37533175779528$	$0.94430$	$4.02778$	$[1, 1, 0, 3740, -279752]$	\(y^2+xy=x^3+x^2+3740x-279752\)	2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.?	$[(67, 493)]$
14586.d1	14586f1	14586.d	14586f	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{2} \cdot 11^{4} \cdot 13^{4} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.4	2B	$136$	$12$	$0$	$0.691213679$	$1$		$7$	$150528$	$1.605587$	$6793805286030262681/1048227429629952$	$0.98644$	$4.52267$	$[1, 0, 1, -39458, 2580212]$	\(y^2+xy+y=x^3-39458x+2580212\)	2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.?	$[(-51, 2137)]$
14586.d2	14586f2	14586.d	14586f	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{7} \cdot 3^{4} \cdot 11^{8} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$136$	$12$	$0$	$0.345606839$	$1$		$10$	$301056$	$1.952160$	$35862531227445945959/108547797844556928$	$1.00994$	$4.84662$	$[1, 0, 1, 68702, 14261492]$	\(y^2+xy+y=x^3+68702x+14261492\)	2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.?	$[(-14, 3653)]$
14586.e1	14586h3	14586.e	14586h	$4$	$6$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( 2^{24} \cdot 3 \cdot 11 \cdot 13^{6} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$2244$	$96$	$1$	$5.592678213$	$1$		$1$	$456192$	$2.432064$	$3957101249824708884951625/772310238681366528$	$0.99739$	$5.90724$	$[1, 0, 1, -3295221, -2302254848]$	\(y^2+xy+y=x^3-3295221x-2302254848\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 66.48.0-66.b.1.3, 68.6.0.b.1, $\ldots$	$[(-207077/14, 327697/14)]$
14586.e2	14586h4	14586.e	14586h	$4$	$6$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{12} \cdot 3^{2} \cdot 11^{2} \cdot 13^{12} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$2244$	$96$	$1$	$2.796339106$	$1$		$0$	$912384$	$2.778641$	$-2830680648734534916567625/1766676274677722124288$	$1.00284$	$5.94861$	$[1, 0, 1, -2947061, -2807643904]$	\(y^2+xy+y=x^3-2947061x-2807643904\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 68.6.0.a.1, 132.48.0.?, $\ldots$	$[(32395/3, 4872674/3)]$
14586.e3	14586h1	14586.e	14586h	$4$	$6$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{3} \cdot 11^{3} \cdot 13^{2} \cdot 17^{6} \)	$1$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$2244$	$96$	$1$	$1.864226071$	$1$		$9$	$152064$	$1.882759$	$111675519439697265625/37528570137307392$	$1.12088$	$4.81467$	$[1, 0, 1, -100326, 7911736]$	\(y^2+xy+y=x^3-100326x+7911736\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 66.48.0-66.b.1.4, 68.6.0.b.1, $\ldots$	$[(-340, 1827)]$
14586.e4	14586h2	14586.e	14586h	$4$	$6$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{4} \cdot 3^{6} \cdot 11^{6} \cdot 13^{4} \cdot 17^{3} \)	$1$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$2244$	$96$	$1$	$0.932113035$	$1$		$16$	$304128$	$2.229332$	$2773679829880629422375/2899504554614368272$	$0.98697$	$5.14971$	$[1, 0, 1, 292714, 54762104]$	\(y^2+xy+y=x^3+292714x+54762104\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 68.6.0.a.1, 132.48.0.?, $\ldots$	$[(-63, 6037)]$
14586.f1	14586d1	14586.f	14586d	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{7} \cdot 3^{12} \cdot 11 \cdot 13 \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1144$	$2$	$0$	$0.283425299$	$1$		$6$	$34944$	$1.078346$	$-1449073218392281/2811246362496$	$0.92302$	$3.79444$	$[1, 0, 1, -2358, 91720]$	\(y^2+xy+y=x^3-2358x+91720\)	1144.2.0.?	$[(20, 219)]$
14586.g1	14586e1	14586.g	14586e	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{2} \cdot 3^{5} \cdot 11 \cdot 13 \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$29172$	$2$	$0$	$0.255307693$	$1$		$6$	$2400$	$-0.097704$	$18191447/2362932$	$0.84393$	$2.30769$	$[1, 0, 1, 5, 74]$	\(y^2+xy+y=x^3+5x+74\)	29172.2.0.?	$[(1, 8)]$
14586.h1	14586g1	14586.h	14586g	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( 2^{4} \cdot 3 \cdot 11 \cdot 13^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$		$1$	$6400$	$0.128754$	$90458382169/25788048$	$0.96781$	$2.63127$	$[1, 0, 1, -94, -256]$	\(y^2+xy+y=x^3-94x-256\)	2.3.0.a.1, 66.6.0.a.1, 68.6.0.b.1, 2244.12.0.?	$[]$
14586.h2	14586g2	14586.h	14586g	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{2} \cdot 3^{2} \cdot 11^{2} \cdot 13^{4} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$		$0$	$12800$	$0.475327$	$1656015369191/2114999172$	$0.87319$	$2.95412$	$[1, 0, 1, 246, -1616]$	\(y^2+xy+y=x^3+246x-1616\)	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[]$
14586.i1	14586k3	14586.i	14586k	$4$	$4$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( 2^{9} \cdot 3^{4} \cdot 11 \cdot 13^{12} \cdot 17^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$3432$	$48$	$0$	$1$	$1$		$0$	$9455616$	$3.927998$	$1748094148784980747354970849498497/887694600425282263291392$	$1.04320$	$7.98345$	$[1, 1, 1, -2509653144, -48392477978535]$	\(y^2+xy+y=x^3+x^2-2509653144x-48392477978535\)	2.3.0.a.1, 4.12.0-4.c.1.2, 88.24.0.?, 312.24.0.?, 3432.48.0.?	$[]$
14586.i2	14586k4	14586.i	14586k	$4$	$4$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( 2^{9} \cdot 3 \cdot 11 \cdot 13^{3} \cdot 17^{16} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$3432$	$48$	$0$	$1$	$4$	$2$	$0$	$9455616$	$3.927998$	$4474676144192042711273397261697/1806328356954994499451382272$	$1.04089$	$7.36101$	$[1, 1, 1, -343304344, 1346305732697]$	\(y^2+xy+y=x^3+x^2-343304344x+1346305732697\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 88.24.0.?, 156.12.0.?, $\ldots$	$[]$
14586.i3	14586k2	14586.i	14586k	$4$	$4$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{2} \cdot 11^{2} \cdot 13^{6} \cdot 17^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$3432$	$48$	$0$	$1$	$1$		$2$	$4727808$	$3.581425$	$433744050935826360922067531137/9612122270219882316693504$	$1.05817$	$7.11760$	$[1, 1, 1, -157701784, -747588108199]$	\(y^2+xy+y=x^3+x^2-157701784x-747588108199\)	2.6.0.a.1, 4.12.0-2.a.1.1, 88.24.0.?, 156.24.0.?, 3432.48.0.?	$[]$
14586.i4	14586k1	14586.i	14586k	$4$	$4$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{36} \cdot 3 \cdot 11^{4} \cdot 13^{3} \cdot 17^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$3432$	$48$	$0$	$1$	$1$		$3$	$2363904$	$3.234852$	$79374649975090937760383/553856914190911653543936$	$1.10385$	$6.47966$	$[1, 1, 1, 895336, -35804233639]$	\(y^2+xy+y=x^3+x^2+895336x-35804233639\)	2.3.0.a.1, 4.12.0-4.c.1.1, 78.6.0.?, 88.24.0.?, 156.24.0.?, $\ldots$	$[]$
14586.j1	14586l1	14586.j	14586l	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{13} \cdot 3^{4} \cdot 11^{7} \cdot 13 \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1144$	$2$	$0$	$0.111118298$	$1$		$10$	$128128$	$1.880720$	$165568631260031/48580832601759744$	$1.05610$	$4.78490$	$[1, 1, 1, 1144, -10604023]$	\(y^2+xy+y=x^3+x^2+1144x-10604023\)	1144.2.0.?	$[(381, 6541)]$
14586.k1	14586j1	14586.k	14586j	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{7} \cdot 11 \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1.580176936$	$1$		$7$	$59136$	$1.484674$	$66342819962001390625/4812668669952$	$0.99193$	$4.76035$	$[1, 1, 1, -84338, -9461761]$	\(y^2+xy+y=x^3+x^2-84338x-9461761\)	2.3.0.a.1, 66.6.0.a.1, 68.6.0.b.1, 2244.12.0.?	$[(-169, 97)]$
14586.k2	14586j2	14586.k	14586j	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2^{6} \cdot 3^{14} \cdot 11^{2} \cdot 13^{4} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2244$	$12$	$0$	$3.160353872$	$1$		$4$	$118272$	$1.831249$	$-54315282059491182625/17983956399469632$	$0.96250$	$4.78668$	$[1, 1, 1, -78898, -10728193]$	\(y^2+xy+y=x^3+x^2-78898x-10728193\)	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(375, 3361)]$
14586.l1	14586i1	14586.l	14586i	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 13 \cdot 17 \)	\( - 2 \cdot 3^{4} \cdot 11 \cdot 13^{3} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1144$	$2$	$0$	$1.790457339$	$1$		$0$	$7296$	$0.424609$	$1259362112399/1131450606$	$0.87057$	$2.90594$	$[1, 1, 1, 225, 1059]$	\(y^2+xy+y=x^3+x^2+225x+1059\)	1144.2.0.?	$[(7/2, 295/2)]$