Elliptic curves over $\Q$ of conductor 28900

Results (18 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
28900.a1	28900e1	28900.a	28900e	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( 2^{8} \cdot 5^{7} \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1$	$1$		$0$	$36288$	$0.820255$	$8912896/5$	$0.97434$	$3.58963$	$[0, 1, 0, -4533, -118937]$	\(y^2=x^3+x^2-4533x-118937\)	10.2.0.a.1	$[]$
28900.b1	28900d3	28900.b	28900d	$4$	$6$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( 2^{4} \cdot 5^{9} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.3, 3.4.0.1	2B, 3B	$2040$	$384$	$9$	$1$	$1$		$1$	$165888$	$1.840681$	$488095744/125$	$1.07376$	$4.81274$	$[0, 1, 0, -298633, -62899512]$	\(y^2=x^3+x^2-298633x-62899512\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 10.6.0.a.1, $\ldots$	$[]$
28900.b2	28900d4	28900.b	28900d	$4$	$6$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{12} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.5, 3.4.0.1	2B, 3B	$2040$	$384$	$9$	$1$	$1$		$1$	$331776$	$2.187256$	$-20720464/15625$	$0.95894$	$4.85630$	$[0, 1, 0, -262508, -78650012]$	\(y^2=x^3+x^2-262508x-78650012\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.24.0.d.1, $\ldots$	$[]$
28900.b3	28900d1	28900.b	28900d	$4$	$6$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( 2^{4} \cdot 5^{7} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.3, 3.4.0.1	2B, 3B	$2040$	$384$	$9$	$1$	$1$		$1$	$55296$	$1.291376$	$16384/5$	$0.95621$	$3.80978$	$[0, 1, 0, -9633, 246988]$	\(y^2=x^3+x^2-9633x+246988\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 10.6.0.a.1, $\ldots$	$[]$
28900.b4	28900d2	28900.b	28900d	$4$	$6$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{8} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.5, 3.4.0.1	2B, 3B	$2040$	$384$	$9$	$1$	$1$		$1$	$110592$	$1.637949$	$21296/25$	$0.83964$	$4.10798$	$[0, 1, 0, 26492, 1691988]$	\(y^2=x^3+x^2+26492x+1691988\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.24.0.d.1, $\ldots$	$[]$
28900.c1	28900i2	28900.c	28900i	$2$	$3$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{8} \cdot 17^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$204$	$16$	$0$	$9.943643281$	$1$		$0$	$311040$	$2.426189$	$-115431760/4913$	$0.96165$	$5.26258$	$[0, -1, 0, -1360708, -632550088]$	\(y^2=x^3-x^2-1360708x-632550088\)	3.4.0.a.1, 12.8.0-3.a.1.4, 51.8.0-3.a.1.1, 68.2.0.a.1, 204.16.0.?	$[(239269/13, 36557344/13)]$
28900.c2	28900i1	28900.c	28900i	$2$	$3$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{8} \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$204$	$16$	$0$	$3.314547760$	$1$		$2$	$103680$	$1.876883$	$27440/17$	$0.71045$	$4.44329$	$[0, -1, 0, 84292, -2530088]$	\(y^2=x^3-x^2+84292x-2530088\)	3.4.0.a.1, 12.8.0-3.a.1.3, 51.8.0-3.a.1.2, 68.2.0.a.1, 204.16.0.?	$[(1026, 34102)]$
28900.d1	28900j1	28900.d	28900j	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{9} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.5.0.1	5S4	$20$	$10$	$0$	$0.709460169$	$1$		$4$	$30240$	$0.827125$	$-272$	$0.77446$	$3.24170$	$[0, -1, 0, -708, 19912]$	\(y^2=x^3-x^2-708x+19912\)	5.5.0.a.1, 20.10.0.b.1	$[(42, 250)]$
28900.e1	28900l1	28900.e	28900l	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{3} \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.5.0.1	5S4	$20$	$10$	$0$	$1$	$1$		$0$	$102816$	$1.439013$	$-272$	$0.77446$	$3.95655$	$[0, -1, 0, -8188, 776072]$	\(y^2=x^3-x^2-8188x+776072\)	5.5.0.a.1, 20.10.0.b.1	$[]$
28900.f1	28900b1	28900.f	28900b	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( 2^{4} \cdot 5^{7} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.24	2B	$680$	$48$	$0$	$1$	$1$		$1$	$165888$	$1.769779$	$151732224/85$	$1.02320$	$4.69899$	$[0, 0, 0, -202300, 35005125]$	\(y^2=x^3-202300x+35005125\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.4, 170.6.0.?, 340.24.0.?, $\ldots$	$[]$
28900.f2	28900b2	28900.f	28900b	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{8} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.38	2B	$680$	$48$	$0$	$1$	$1$		$1$	$331776$	$2.116352$	$-5256144/7225$	$0.89008$	$4.75997$	$[0, 0, 0, -166175, 47901750]$	\(y^2=x^3-166175x+47901750\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.2, 340.12.0.?, 680.48.0.?	$[]$
28900.g1	28900f1	28900.g	28900f	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( 2^{8} \cdot 5^{11} \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.5.0.1	5S4	$10$	$30$	$0$	$5.702947961$	$1$		$0$	$440640$	$2.561405$	$30081024/3125$	$1.04213$	$5.36303$	$[0, 0, 0, -1965200, -960491500]$	\(y^2=x^3-1965200x-960491500\)	5.5.0.a.1, 10.30.0.a.1, 20.120.6.a.1	$[(-62135/8, 2911675/8)]$
28900.h1	28900a1	28900.h	28900a	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( 2^{8} \cdot 5^{11} \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.5.0.1	5S4	$10$	$30$	$0$	$1$	$1$		$0$	$25920$	$1.144796$	$30081024/3125$	$1.04213$	$3.70805$	$[0, 0, 0, -6800, -195500]$	\(y^2=x^3-6800x-195500\)	5.5.0.a.1, 10.30.0.a.1, 20.120.6.a.1	$[]$
28900.i1	28900h1	28900.i	28900h	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{3} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.5.0.1	5S4	$20$	$10$	$0$	$1.290375076$	$1$		$2$	$6048$	$0.022406$	$-272$	$0.77446$	$2.30157$	$[0, 1, 0, -28, 148]$	\(y^2=x^3+x^2-28x+148\)	5.5.0.a.1, 20.10.0.b.1	$[(3, 10)]$
28900.j1	28900k1	28900.j	28900k	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{9} \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.5.0.1	5S4	$20$	$10$	$0$	$1$	$1$		$0$	$514080$	$2.243732$	$-272$	$0.77446$	$4.89668$	$[0, 1, 0, -204708, 96599588]$	\(y^2=x^3+x^2-204708x+96599588\)	5.5.0.a.1, 20.10.0.b.1	$[]$
28900.k1	28900c2	28900.k	28900c	$2$	$3$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{2} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1020$	$16$	$0$	$1$	$1$		$0$	$62208$	$1.621469$	$-115431760/4913$	$0.96165$	$4.32245$	$[0, 1, 0, -54428, -5082172]$	\(y^2=x^3+x^2-54428x-5082172\)	3.4.0.a.1, 60.8.0-3.a.1.3, 68.2.0.a.1, 204.8.0.?, 255.8.0.?, $\ldots$	$[]$
28900.k2	28900c1	28900.k	28900c	$2$	$3$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{8} \cdot 5^{2} \cdot 17^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1020$	$16$	$0$	$1$	$1$		$0$	$20736$	$1.072165$	$27440/17$	$0.71045$	$3.50316$	$[0, 1, 0, 3372, -18892]$	\(y^2=x^3+x^2+3372x-18892\)	3.4.0.a.1, 60.8.0-3.a.1.4, 68.2.0.a.1, 204.8.0.?, 255.8.0.?, $\ldots$	$[]$
28900.l1	28900g1	28900.l	28900g	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 17^{2} \)	\( 2^{8} \cdot 5^{7} \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$4.563367483$	$1$		$0$	$616896$	$2.236862$	$8912896/5$	$0.97434$	$5.24461$	$[0, -1, 0, -1310133, -576476863]$	\(y^2=x^3-x^2-1310133x-576476863\)	10.2.0.a.1	$[(-96767/12, 223975/12)]$