Elliptic curves over $\Q$ of conductor 2006

Results (15 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
2006.a1	2006d1	2006.a	2006d	$1$	$1$	\( 2 \cdot 17 \cdot 59 \)	\( - 2^{2} \cdot 17^{2} \cdot 59 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$118$	$2$	$0$	$0.152944298$	$1$		$20$	$384$	$-0.147431$	$-76711450249/68204$	$0.84709$	$3.29632$	$[1, 1, 0, -88, 284]$	\(y^2+xy=x^3+x^2-88x+284\)	118.2.0.?	$[(7, 5), (4, 2)]$
2006.b1	2006b1	2006.b	2006b	$1$	$1$	\( 2 \cdot 17 \cdot 59 \)	\( - 2^{18} \cdot 17^{4} \cdot 59 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$118$	$2$	$0$	$1.146960230$	$1$		$4$	$2304$	$1.004854$	$111416568869159/1291777212416$	$0.95186$	$4.64111$	$[1, 1, 0, 1003, -52883]$	\(y^2+xy=x^3+x^2+1003x-52883\)	118.2.0.?	$[(42, 235)]$
2006.c1	2006e1	2006.c	2006e	$1$	$1$	\( 2 \cdot 17 \cdot 59 \)	\( - 2^{23} \cdot 17^{5} \cdot 59 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8024$	$2$	$0$	$1$	$9$	$3$	$0$	$154560$	$2.800980$	$-21907234671397038959171876713/702726803554304$	$1.03446$	$8.58200$	$[1, 1, 0, -58293654, -171333232940]$	\(y^2+xy=x^3+x^2-58293654x-171333232940\)	8024.2.0.?	$[]$
2006.d1	2006a1	2006.d	2006a	$2$	$2$	\( 2 \cdot 17 \cdot 59 \)	\( 2^{2} \cdot 17 \cdot 59^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.4	2B	$136$	$12$	$0$	$2.913057303$	$1$		$3$	$560$	$0.315628$	$206896959473625/236708$	$1.08343$	$4.33505$	$[1, -1, 0, -1232, -16340]$	\(y^2+xy=x^3-x^2-1232x-16340\)	2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.?	$[(180, 2270)]$
2006.d2	2006a2	2006.d	2006a	$2$	$2$	\( 2 \cdot 17 \cdot 59 \)	\( - 2 \cdot 17^{2} \cdot 59^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$136$	$12$	$0$	$5.826114607$	$1$		$0$	$1120$	$0.662202$	$-201900421229625/7003834658$	$1.08431$	$4.33949$	$[1, -1, 0, -1222, -16626]$	\(y^2+xy=x^3-x^2-1222x-16626\)	2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.?	$[(1077/4, 26661/4)]$
2006.e1	2006c2	2006.e	2006c	$2$	$3$	\( 2 \cdot 17 \cdot 59 \)	\( - 2^{12} \cdot 17^{2} \cdot 59^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$354$	$16$	$0$	$1$	$1$		$0$	$4992$	$1.215673$	$-2281081786314874633/243116158976$	$0.96227$	$5.55917$	$[1, 0, 1, -27425, -1750508]$	\(y^2+xy+y=x^3-27425x-1750508\)	3.8.0-3.a.1.1, 118.2.0.?, 354.16.0.?	$[]$
2006.e2	2006c1	2006.e	2006c	$2$	$3$	\( 2 \cdot 17 \cdot 59 \)	\( - 2^{4} \cdot 17^{6} \cdot 59 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$354$	$16$	$0$	$1$	$1$		$2$	$1664$	$0.666367$	$3131359847/22785865136$	$0.98930$	$4.11684$	$[1, 0, 1, 30, -7260]$	\(y^2+xy+y=x^3+30x-7260\)	3.8.0-3.a.1.2, 118.2.0.?, 354.16.0.?	$[]$
2006.f1	2006f1	2006.f	2006f	$1$	$1$	\( 2 \cdot 17 \cdot 59 \)	\( - 2^{7} \cdot 17 \cdot 59 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$8024$	$2$	$0$	$1$	$1$		$0$	$448$	$-0.250021$	$-3354790473/128384$	$0.82685$	$2.89295$	$[1, -1, 0, -31, 77]$	\(y^2+xy=x^3-x^2-31x+77\)	8024.2.0.?	$[]$
2006.g1	2006k1	2006.g	2006k	$1$	$1$	\( 2 \cdot 17 \cdot 59 \)	\( - 2^{16} \cdot 17^{2} \cdot 59 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$118$	$2$	$0$	$0.089486659$	$1$		$12$	$1536$	$0.421446$	$715236537807/1117454336$	$0.91484$	$3.65949$	$[1, -1, 1, 186, -1323]$	\(y^2+xy+y=x^3-x^2+186x-1323\)	118.2.0.?	$[(41, 251)]$
2006.h1	2006j1	2006.h	2006j	$1$	$1$	\( 2 \cdot 17 \cdot 59 \)	\( - 2^{4} \cdot 17^{2} \cdot 59 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$118$	$2$	$0$	$0.338322676$	$1$		$6$	$256$	$-0.264764$	$-192100033/272816$	$0.80553$	$2.67140$	$[1, 1, 1, -12, -35]$	\(y^2+xy+y=x^3+x^2-12x-35\)	118.2.0.?	$[(7, 13)]$
2006.i1	2006g1	2006.i	2006g	$1$	$1$	\( 2 \cdot 17 \cdot 59 \)	\( - 2^{30} \cdot 17^{4} \cdot 59 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$118$	$2$	$0$	$1$	$1$		$0$	$57600$	$2.584869$	$-466534433251600609479662161/5291119462055936$	$1.02559$	$8.07578$	$[1, 1, 1, -16157965, -25006047741]$	\(y^2+xy+y=x^3+x^2-16157965x-25006047741\)	118.2.0.?	$[]$
2006.j1	2006i2	2006.j	2006i	$2$	$2$	\( 2 \cdot 17 \cdot 59 \)	\( 2 \cdot 17^{2} \cdot 59 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$8024$	$12$	$0$	$2.695260074$	$1$		$0$	$480$	$0.149659$	$27612067640625/34102$	$1.00958$	$4.07019$	$[1, -1, 1, -630, 6239]$	\(y^2+xy+y=x^3-x^2-630x+6239\)	2.3.0.a.1, 68.6.0.c.1, 472.6.0.?, 8024.12.0.?	$[(63/2, -13/2)]$
2006.j2	2006i1	2006.j	2006i	$2$	$2$	\( 2 \cdot 17 \cdot 59 \)	\( 2^{2} \cdot 17 \cdot 59^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$8024$	$12$	$0$	$1.347630037$	$1$		$3$	$240$	$-0.196915$	$6913292625/236708$	$0.83603$	$2.97962$	$[1, -1, 1, -40, 103]$	\(y^2+xy+y=x^3-x^2-40x+103\)	2.3.0.a.1, 34.6.0.a.1, 472.6.0.?, 8024.12.0.?	$[(1, 7)]$
2006.k1	2006h2	2006.k	2006h	$2$	$2$	\( 2 \cdot 17 \cdot 59 \)	\( 2^{6} \cdot 17^{10} \cdot 59 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$4012$	$12$	$0$	$1$	$4$	$2$	$0$	$14400$	$1.737589$	$13592251860742707697/7612392968095424$	$1.00818$	$5.79387$	$[1, 1, 1, -49719, -786739]$	\(y^2+xy+y=x^3+x^2-49719x-786739\)	2.3.0.a.1, 68.6.0.c.1, 236.6.0.?, 4012.12.0.?	$[]$
2006.k2	2006h1	2006.k	2006h	$2$	$2$	\( 2 \cdot 17 \cdot 59 \)	\( 2^{12} \cdot 17^{5} \cdot 59^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$4012$	$12$	$0$	$1$	$1$		$1$	$7200$	$1.391016$	$3243586268529106417/20244571000832$	$0.96397$	$5.60544$	$[1, 1, 1, -30839, 2060365]$	\(y^2+xy+y=x^3+x^2-30839x+2060365\)	2.3.0.a.1, 34.6.0.a.1, 236.6.0.?, 4012.12.0.?	$[]$