Elliptic curves over $\Q$ of conductor 100016

Results (27 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
100016.a1	100016a1	100016.a	100016a	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{8} \cdot 7 \cdot 19^{2} \cdot 47 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$25004$	$12$	$0$	$2.249172616$	$1$		$3$	$19712$	$0.130702$	$259108432/118769$	$0.70398$	$2.16431$	$[0, 1, 0, -84, -164]$	\(y^2=x^3+x^2-84x-164\)	2.3.0.a.1, 76.6.0.?, 658.6.0.?, 25004.12.0.?	$[(14, 40)]$
100016.a2	100016a2	100016.a	100016a	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{10} \cdot 7^{2} \cdot 19 \cdot 47^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$25004$	$12$	$0$	$1.124586308$	$1$		$5$	$39424$	$0.477276$	$2791456412/2056579$	$0.76733$	$2.49119$	$[0, 1, 0, 296, -924]$	\(y^2=x^3+x^2+296x-924\)	2.3.0.a.1, 38.6.0.b.1, 1316.6.0.?, 25004.12.0.?	$[(10, 56)]$
100016.b1	100016e2	100016.b	100016e	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{8} \cdot 7 \cdot 19^{2} \cdot 47^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$25004$	$12$	$0$	$1$	$1$		$1$	$1168128$	$2.105553$	$25156640481643577374288/262360721$	$0.95317$	$4.96171$	$[0, 1, 0, -3876052, -2938485540]$	\(y^2=x^3+x^2-3876052x-2938485540\)	2.3.0.a.1, 76.6.0.?, 658.6.0.?, 25004.12.0.?	$[]$
100016.b2	100016e1	100016.b	100016e	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{4} \cdot 7^{2} \cdot 19 \cdot 47^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$25004$	$12$	$0$	$1$	$1$		$1$	$584064$	$1.758978$	$-98260901558505084928/10035449471299$	$0.94584$	$4.23926$	$[0, 1, 0, -242247, -45976760]$	\(y^2=x^3+x^2-242247x-45976760\)	2.3.0.a.1, 38.6.0.b.1, 1316.6.0.?, 25004.12.0.?	$[]$
100016.c1	100016o1	100016.c	100016o	$1$	$1$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{16} \cdot 7^{7} \cdot 19^{4} \cdot 47 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1316$	$2$	$0$	$1$	$1$		$0$	$1462272$	$2.308685$	$-143563142482697477233/80708360371856$	$0.94318$	$4.75390$	$[0, -1, 0, -1745392, -887388736]$	\(y^2=x^3-x^2-1745392x-887388736\)	1316.2.0.?	$[]$
100016.d1	100016n1	100016.d	100016n	$1$	$1$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{16} \cdot 7 \cdot 19 \cdot 47 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12502$	$2$	$0$	$0.745134110$	$1$		$4$	$36864$	$0.347775$	$-95443993/100016$	$0.73623$	$2.40815$	$[0, -1, 0, -152, 1264]$	\(y^2=x^3-x^2-152x+1264\)	12502.2.0.?	$[(12, 32)]$
100016.e1	100016h1	100016.e	100016h	$1$	$1$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{4} \cdot 7^{7} \cdot 19 \cdot 47 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12502$	$2$	$0$	$0.765042535$	$1$		$4$	$43008$	$0.613301$	$62800480256/735423899$	$0.84357$	$2.65720$	$[0, -1, 0, 209, -5158]$	\(y^2=x^3-x^2+209x-5158\)	12502.2.0.?	$[(22, 98)]$
100016.f1	100016f1	100016.f	100016f	$1$	$1$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12502$	$2$	$0$	$1.646800567$	$1$		$2$	$7680$	$-0.248955$	$-304900096/6251$	$0.69395$	$1.94065$	$[0, -1, 0, -35, 94]$	\(y^2=x^3-x^2-35x+94\)	12502.2.0.?	$[(6, 8)]$
100016.g1	100016m1	100016.g	100016m	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{14} \cdot 7^{3} \cdot 19^{2} \cdot 47 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$50008$	$12$	$0$	$3.138258121$	$1$		$3$	$80640$	$0.944548$	$3733252610697/23278724$	$0.93119$	$3.23684$	$[0, 0, 0, -5171, -142350]$	\(y^2=x^3-5171x-142350\)	2.3.0.a.1, 152.6.0.?, 658.6.0.?, 50008.12.0.?	$[(89, 320)]$
100016.g2	100016m2	100016.g	100016m	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{13} \cdot 7^{6} \cdot 19 \cdot 47^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$50008$	$12$	$0$	$6.276516243$	$1$		$1$	$161280$	$1.291121$	$-261284780457/9875692358$	$0.93608$	$3.37017$	$[0, 0, 0, -2131, -308334]$	\(y^2=x^3-2131x-308334\)	2.3.0.a.1, 152.6.0.?, 1316.6.0.?, 50008.12.0.?	$[(337/2, 2655/2)]$
100016.h1	100016p4	100016.h	100016p	$4$	$4$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{13} \cdot 7^{4} \cdot 19^{2} \cdot 47^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.49	2B	$2632$	$48$	$0$	$1.492748857$	$1$		$11$	$454656$	$1.876106$	$25172562615580017/8459034366482$	$0.92723$	$4.00260$	$[0, 0, 0, -97691, 7610314]$	\(y^2=x^3-97691x+7610314\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.k.1.2, 2632.48.0.?	$[(309, 2632)]$
100016.h2	100016p2	100016.h	100016p	$4$	$4$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{14} \cdot 7^{2} \cdot 19^{4} \cdot 47^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.2	2Cs	$2632$	$48$	$0$	$2.985497715$	$1$		$7$	$227328$	$1.529531$	$1719073016770257/56424301444$	$0.95895$	$3.76948$	$[0, 0, 0, -39931, -2982870]$	\(y^2=x^3-39931x-2982870\)	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.1, 1316.24.0.?, 2632.48.0.?	$[(-113, 294)]$
100016.h3	100016p1	100016.h	100016p	$4$	$4$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{16} \cdot 7 \cdot 19^{2} \cdot 47 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.60	2B	$2632$	$48$	$0$	$5.970995431$	$1$		$1$	$113664$	$1.182959$	$1678074290715537/1900304$	$0.89842$	$3.76738$	$[0, 0, 0, -39611, -3034390]$	\(y^2=x^3-39611x-3034390\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.3, 658.6.0.?, 1316.24.0.?, $\ldots$	$[(2101/3, 17920/3)]$
100016.h4	100016p3	100016.h	100016p	$4$	$4$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{13} \cdot 7 \cdot 19^{8} \cdot 47 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.101	2B	$2632$	$48$	$0$	$5.970995431$	$1$		$3$	$454656$	$1.876106$	$55424004754383/11175184480978$	$1.02907$	$3.97933$	$[0, 0, 0, 12709, -10278774]$	\(y^2=x^3+12709x-10278774\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.5, 1316.12.0.?, 2632.48.0.?	$[(639, 16086)]$
100016.i1	100016k2	100016.i	100016k	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{8} \cdot 7^{5} \cdot 19^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$25004$	$12$	$0$	$8.800510880$	$1$		$1$	$253440$	$1.484840$	$314246148685362000/13402725343$	$0.94264$	$3.98105$	$[0, 0, 0, -89935, 10380666]$	\(y^2=x^3-89935x+10380666\)	2.3.0.a.1, 28.6.0.a.1, 3572.6.0.?, 25004.12.0.?	$[(31513/18, 9319301/18)]$
100016.i2	100016k1	100016.i	100016k	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{4} \cdot 7^{10} \cdot 19 \cdot 47 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$25004$	$12$	$0$	$17.60102176$	$1$		$1$	$126720$	$1.138268$	$1419579648000000/252250397357$	$1.01584$	$3.27121$	$[0, 0, 0, -5900, 145203]$	\(y^2=x^3-5900x+145203\)	2.3.0.a.1, 28.6.0.b.1, 1786.6.0.?, 25004.12.0.?	$[(14675833/828, 96192971443/828)]$
100016.j1	100016l1	100016.j	100016l	$1$	$1$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{13} \cdot 7 \cdot 19 \cdot 47 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$50008$	$2$	$0$	$1.370638804$	$1$		$2$	$14976$	$0.167449$	$16581375/12502$	$0.70087$	$2.16637$	$[0, 0, 0, 85, -166]$	\(y^2=x^3+85x-166\)	50008.2.0.?	$[(13, 56)]$
100016.k1	100016b4	100016.k	100016b	$4$	$4$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{10} \cdot 7 \cdot 19^{4} \cdot 47 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$50008$	$48$	$0$	$1$	$1$		$1$	$84992$	$0.957428$	$39294874074852/42875609$	$0.98376$	$3.32088$	$[0, 0, 0, -7139, -231950]$	\(y^2=x^3-7139x-231950\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 152.12.0.?, 188.12.0.?, $\ldots$	$[]$
100016.k2	100016b2	100016.k	100016b	$4$	$4$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{8} \cdot 7^{2} \cdot 19^{2} \cdot 47^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$25004$	$48$	$0$	$1$	$1$		$3$	$42496$	$0.610854$	$75460411728/39075001$	$0.90955$	$2.65715$	$[0, 0, 0, -559, -1650]$	\(y^2=x^3-559x-1650\)	2.6.0.a.1, 28.12.0-2.a.1.1, 76.12.0.?, 188.12.0.?, 532.24.0.?, $\ldots$	$[]$
100016.k3	100016b1	100016.k	100016b	$4$	$4$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{4} \cdot 7^{4} \cdot 19 \cdot 47 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$50008$	$48$	$0$	$1$	$1$		$1$	$21248$	$0.264281$	$213989603328/2144093$	$0.80151$	$2.50687$	$[0, 0, 0, -314, 2123]$	\(y^2=x^3-314x+2123\)	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.5, 76.12.0.?, 188.12.0.?, $\ldots$	$[]$
100016.k4	100016b3	100016.k	100016b	$4$	$4$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{10} \cdot 7 \cdot 19 \cdot 47^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$50008$	$48$	$0$	$1$	$1$		$1$	$84992$	$0.957428$	$1001617520508/648997573$	$0.89222$	$3.00216$	$[0, 0, 0, 2101, -12822]$	\(y^2=x^3+2101x-12822\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 76.12.0.?, 376.12.0.?, $\ldots$	$[]$
100016.l1	100016c1	100016.l	100016c	$1$	$1$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{8} \cdot 7^{11} \cdot 19^{3} \cdot 47 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12502$	$2$	$0$	$1$	$1$		$0$	$743424$	$1.993183$	$-362446969457861584/637436754121139$	$0.91651$	$4.11470$	$[0, 1, 0, -94316, -22437604]$	\(y^2=x^3+x^2-94316x-22437604\)	12502.2.0.?	$[]$
100016.m1	100016j1	100016.m	100016j	$1$	$1$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{8} \cdot 7 \cdot 19^{2} \cdot 47 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1316$	$2$	$0$	$1$	$1$		$0$	$21888$	$0.124840$	$187153328/118769$	$0.71391$	$2.13606$	$[0, 1, 0, 76, 104]$	\(y^2=x^3+x^2+76x+104\)	1316.2.0.?	$[]$
100016.n1	100016i2	100016.n	100016i	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{11} \cdot 7^{2} \cdot 19^{2} \cdot 47^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$2632$	$12$	$0$	$1.552859860$	$1$		$3$	$144384$	$1.092199$	$201569651552306/39075001$	$0.86209$	$3.52310$	$[0, -1, 0, -15512, 748688]$	\(y^2=x^3-x^2-15512x+748688\)	2.3.0.a.1, 8.6.0.b.1, 1316.6.0.?, 2632.12.0.?	$[(496, 10716)]$
100016.n2	100016i1	100016.n	100016i	$2$	$2$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( 2^{10} \cdot 7 \cdot 19^{4} \cdot 47 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$2632$	$12$	$0$	$3.105719720$	$1$		$3$	$72192$	$0.745625$	$133172077252/42875609$	$0.79919$	$2.82690$	$[0, -1, 0, -1072, 9360]$	\(y^2=x^3-x^2-1072x+9360\)	2.3.0.a.1, 8.6.0.c.1, 658.6.0.?, 2632.12.0.?	$[(-18, 150)]$
100016.o1	100016g1	100016.o	100016g	$1$	$1$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{4} \cdot 7 \cdot 19^{3} \cdot 47 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12502$	$2$	$0$	$6.731715376$	$1$		$0$	$46080$	$0.132890$	$-271669248/2256611$	$0.77084$	$2.16484$	$[0, 0, 0, -34, 299]$	\(y^2=x^3-34x+299\)	12502.2.0.?	$[(295/9, 10898/9)]$
100016.p1	100016d1	100016.p	100016d	$1$	$1$	\( 2^{4} \cdot 7 \cdot 19 \cdot 47 \)	\( - 2^{8} \cdot 7^{3} \cdot 19 \cdot 47 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12502$	$2$	$0$	$1$	$1$		$0$	$39936$	$0.215931$	$-472058064/306299$	$0.70303$	$2.28173$	$[0, 0, 0, -103, -586]$	\(y^2=x^3-103x-586\)	12502.2.0.?	$[]$