Elliptic curves over $\Q$ of conductor 20184

Results (25 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
20184.a1	20184n1	20184.a	20184n	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{11} \cdot 3 \cdot 29^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$696$	$2$	$0$	$1$	$1$		$0$	$67200$	$1.374126$	$24334/87$	$0.81241$	$3.99212$	$[0, -1, 0, 6448, -455604]$	\(y^2=x^3-x^2+6448x-455604\)	696.2.0.?	$[]$
20184.b1	20184a1	20184.b	20184a	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{4} \cdot 3^{3} \cdot 29^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$174$	$2$	$0$	$0.591219505$	$1$		$2$	$40320$	$1.162329$	$-562432/783$	$0.80037$	$3.77718$	$[0, -1, 0, -3644, 157485]$	\(y^2=x^3-x^2-3644x+157485\)	174.2.0.?	$[(97, 841)]$
20184.c1	20184b1	20184.c	20184b	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{11} \cdot 3^{6} \cdot 29^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$2.230218899$	$1$		$2$	$14400$	$0.525600$	$26478914/729$	$0.92764$	$3.17282$	$[0, -1, 0, -744, -7380]$	\(y^2=x^3-x^2-744x-7380\)	8.2.0.b.1	$[(33, 54)]$
20184.d1	20184d1	20184.d	20184d	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{4} \cdot 3^{11} \cdot 29^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$174$	$2$	$0$	$1$	$1$		$0$	$714560$	$2.526535$	$-3764768000/177147$	$1.12197$	$5.56919$	$[0, -1, 0, -1991768, 1125738429]$	\(y^2=x^3-x^2-1991768x+1125738429\)	174.2.0.?	$[]$
20184.e1	20184m1	20184.e	20184m	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{4} \cdot 3^{5} \cdot 29^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$174$	$2$	$0$	$1$	$1$		$0$	$67200$	$1.341999$	$10976000/7047$	$0.89158$	$3.95329$	$[0, -1, 0, 9812, 120481]$	\(y^2=x^3-x^2+9812x+120481\)	174.2.0.?	$[]$
20184.f1	20184c2	20184.f	20184c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{11} \cdot 3^{2} \cdot 29^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$696$	$12$	$0$	$1$	$1$		$1$	$6720$	$0.541301$	$3906250/9$	$1.17522$	$3.31946$	$[0, -1, 0, -1208, -15732]$	\(y^2=x^3-x^2-1208x-15732\)	2.3.0.a.1, 24.6.0.j.1, 232.6.0.?, 348.6.0.?, 696.12.0.?	$[]$
20184.f2	20184c1	20184.f	20184c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{10} \cdot 3 \cdot 29^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$696$	$12$	$0$	$1$	$1$		$1$	$3360$	$0.194727$	$-500/3$	$0.83300$	$2.59051$	$[0, -1, 0, -48, -420]$	\(y^2=x^3-x^2-48x-420\)	2.3.0.a.1, 24.6.0.j.1, 174.6.0.?, 232.6.0.?, 696.12.0.?	$[]$
20184.g1	20184l1	20184.g	20184l	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{11} \cdot 3^{10} \cdot 29^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$1$	$16$	$2$	$0$	$19905600$	$4.289536$	$1375088009512735250/59049$	$1.10584$	$8.37946$	$[0, -1, 0, -22044769968, 1259821465648524]$	\(y^2=x^3-x^2-22044769968x+1259821465648524\)	8.2.0.b.1	$[]$
20184.h1	20184k1	20184.h	20184k	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{8} \cdot 3 \cdot 29^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$3120$	$0.044448$	$-3712000/3$	$0.89524$	$2.76498$	$[0, -1, 0, -193, -971]$	\(y^2=x^3-x^2-193x-971\)	6.2.0.a.1	$[]$
20184.i1	20184f5	20184.i	20184f	$6$	$8$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{11} \cdot 3^{2} \cdot 29^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.210	2B	$1392$	$192$	$1$	$1$	$4$	$2$	$1$	$96768$	$1.731443$	$3065617154/9$	$1.21059$	$5.01096$	$[0, 1, 0, -323224, -70837648]$	\(y^2=x^3+x^2-323224x-70837648\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.r.1, 16.48.0.l.1, 24.48.0.bf.1, $\ldots$	$[]$
20184.i2	20184f4	20184.i	20184f	$6$	$8$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{10} \cdot 3 \cdot 29^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.127	2B	$1392$	$192$	$1$	$1$	$1$		$1$	$48384$	$1.384869$	$28756228/3$	$1.05617$	$4.47001$	$[0, 1, 0, -54104, 4825440]$	\(y^2=x^3+x^2-54104x+4825440\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0.h.1, 16.48.0.bb.2, $\ldots$	$[]$
20184.i3	20184f3	20184.i	20184f	$6$	$8$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{10} \cdot 3^{4} \cdot 29^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.88	2Cs	$696$	$192$	$1$	$1$	$1$		$3$	$48384$	$1.384869$	$1556068/81$	$1.03212$	$4.17577$	$[0, 1, 0, -20464, -1081744]$	\(y^2=x^3+x^2-20464x-1081744\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.e.2, 24.96.1.bl.2, 116.24.0.?, $\ldots$	$[]$
20184.i4	20184f2	20184.i	20184f	$6$	$8$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{8} \cdot 3^{2} \cdot 29^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.138	2Cs	$696$	$192$	$1$	$1$	$1$		$3$	$24192$	$1.038296$	$35152/9$	$0.97255$	$3.65355$	$[0, 1, 0, -3644, 62016]$	\(y^2=x^3+x^2-3644x+62016\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.h.1, 12.24.0.c.1, 24.96.1.bu.1, $\ldots$	$[]$
20184.i5	20184f1	20184.i	20184f	$6$	$8$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{4} \cdot 3 \cdot 29^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.150	2B	$1392$	$192$	$1$	$1$	$1$		$1$	$12096$	$0.691722$	$2048/3$	$1.17572$	$3.13005$	$[0, 1, 0, 561, 6510]$	\(y^2=x^3+x^2+561x+6510\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.ba.1, 12.12.0.g.1, $\ldots$	$[]$
20184.i6	20184f6	20184.i	20184f	$6$	$8$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{11} \cdot 3^{8} \cdot 29^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.218	2B	$1392$	$192$	$1$	$1$	$1$		$1$	$96768$	$1.731443$	$207646/6561$	$1.15980$	$4.44417$	$[0, 1, 0, 13176, -4257360]$	\(y^2=x^3+x^2+13176x-4257360\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0.m.1, 48.96.1.w.2, 116.12.0.?, $\ldots$	$[]$
20184.j1	20184g1	20184.j	20184g	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{4} \cdot 3^{7} \cdot 29^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$174$	$2$	$0$	$1$	$1$		$0$	$282240$	$2.077164$	$1192310528/53338743$	$1.01314$	$4.86351$	$[0, 1, 0, 46816, -34041375]$	\(y^2=x^3+x^2+46816x-34041375\)	174.2.0.?	$[]$
20184.k1	20184r1	20184.k	20184r	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{11} \cdot 3^{6} \cdot 29^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$1$	$1$		$0$	$417600$	$2.209248$	$26478914/729$	$0.92764$	$5.21100$	$[0, 1, 0, -625984, -186249760]$	\(y^2=x^3+x^2-625984x-186249760\)	8.2.0.b.1	$[]$
20184.l1	20184q1	20184.l	20184q	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{4} \cdot 3^{11} \cdot 29^{3} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$174$	$2$	$0$	$0.162232252$	$1$		$22$	$24640$	$0.842886$	$-3764768000/177147$	$1.12197$	$3.53100$	$[0, 1, 0, -2368, 45341]$	\(y^2=x^3+x^2-2368x+45341\)	174.2.0.?	$[(-10, 261), (221/2, 2349/2)]$
20184.m1	20184o1	20184.m	20184o	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{4} \cdot 3^{3} \cdot 29^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$174$	$2$	$0$	$0.370396015$	$1$		$2$	$40320$	$1.478479$	$-4764064000/783$	$0.91537$	$4.56599$	$[0, 1, 0, -74288, 7769781]$	\(y^2=x^3+x^2-74288x+7769781\)	174.2.0.?	$[(19, 2523)]$
20184.n1	20184p2	20184.n	20184p	$2$	$2$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{11} \cdot 3^{2} \cdot 29^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$696$	$12$	$0$	$1$	$25$	$5$	$1$	$194880$	$2.224949$	$3906250/9$	$1.17522$	$5.35764$	$[0, 1, 0, -1016208, -393848928]$	\(y^2=x^3+x^2-1016208x-393848928\)	2.3.0.a.1, 24.6.0.j.1, 232.6.0.?, 348.6.0.?, 696.12.0.?	$[]$
20184.n2	20184p1	20184.n	20184p	$2$	$2$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{10} \cdot 3 \cdot 29^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$696$	$12$	$0$	$1$	$25$	$5$	$1$	$97440$	$1.878374$	$-500/3$	$0.83300$	$4.62869$	$[0, 1, 0, -40648, -10648960]$	\(y^2=x^3+x^2-40648x-10648960\)	2.3.0.a.1, 24.6.0.j.1, 174.6.0.?, 232.6.0.?, 696.12.0.?	$[]$
20184.o1	20184i1	20184.o	20184i	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{8} \cdot 3 \cdot 29^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$12.92410219$	$1$		$0$	$90480$	$1.728096$	$-3712000/3$	$0.89524$	$4.80316$	$[0, 1, 0, -162593, -25306749]$	\(y^2=x^3+x^2-162593x-25306749\)	6.2.0.a.1	$[(721411/33, 451914094/33)]$
20184.p1	20184j1	20184.p	20184j	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( 2^{11} \cdot 3^{10} \cdot 29^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$0.647821718$	$1$		$0$	$686400$	$2.605885$	$1375088009512735250/59049$	$1.10584$	$6.34128$	$[0, 1, 0, -26212568, 51646275696]$	\(y^2=x^3+x^2-26212568x+51646275696\)	8.2.0.b.1	$[(11821/2, 261/2)]$
20184.q1	20184e1	20184.q	20184e	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{11} \cdot 3^{5} \cdot 29^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$696$	$2$	$0$	$1$	$1$		$0$	$604800$	$2.568630$	$-11205525764162/5926527$	$0.99101$	$5.83868$	$[0, 1, 0, -4979000, 4276526832]$	\(y^2=x^3+x^2-4979000x+4276526832\)	696.2.0.?	$[]$
20184.r1	20184h1	20184.r	20184h	$1$	$1$	\( 2^{3} \cdot 3 \cdot 29^{2} \)	\( - 2^{4} \cdot 3 \cdot 29^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$174$	$2$	$0$	$1$	$4$	$2$	$0$	$120960$	$1.568628$	$-331527424/73167$	$0.97835$	$4.32969$	$[0, 1, 0, -30556, -2426503]$	\(y^2=x^3+x^2-30556x-2426503\)	174.2.0.?	$[]$