Elliptic curves over $\Q$ of conductor 22743

Results (32 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
22743.a1	22743o2	22743.a	22743o	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{8} \cdot 7 \cdot 19^{12} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$2.667520881$	$1$		$2$	$967680$	$2.547565$	$11192824869409/2963890503$	$0.95644$	$5.41313$	$[1, -1, 1, -1514102, 528518310]$	\(y^2+xy+y=x^3-x^2-1514102x+528518310\)	2.3.0.a.1, 28.6.0.a.1, 228.6.0.?, 1596.12.0.?	$[(-223, 29352)]$
22743.a2	22743o1	22743.a	22743o	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{7} \cdot 7^{2} \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.333760440$	$1$		$3$	$483840$	$2.200993$	$8855610342769/1008273$	$0.94565$	$5.38978$	$[1, -1, 1, -1400387, 638139570]$	\(y^2+xy+y=x^3-x^2-1400387x+638139570\)	2.3.0.a.1, 28.6.0.b.1, 114.6.0.?, 1596.12.0.?	$[(2228, 91482)]$
22743.b1	22743f1	22743.b	22743f	$1$	$1$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{9} \cdot 7 \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$84$	$2$	$0$	$1$	$1$		$0$	$114912$	$1.653946$	$-13851/7$	$0.67892$	$4.34677$	$[1, -1, 1, -34724, -3400028]$	\(y^2+xy+y=x^3-x^2-34724x-3400028\)	84.2.0.?	$[]$
22743.c1	22743d2	22743.c	22743d	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{3} \cdot 7^{2} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.071491442$	$1$		$6$	$5120$	$0.201845$	$15438249/49$	$0.87469$	$2.85900$	$[1, -1, 1, -296, -1878]$	\(y^2+xy+y=x^3-x^2-296x-1878\)	2.3.0.a.1, 28.6.0.d.1, 114.6.0.?, 1596.12.0.?	$[(-10, 6)]$
22743.c2	22743d1	22743.c	22743d	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{3} \cdot 7 \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$2.142982885$	$1$		$5$	$2560$	$-0.144728$	$-729/7$	$0.74333$	$2.15194$	$[1, -1, 1, -11, -54]$	\(y^2+xy+y=x^3-x^2-11x-54\)	2.3.0.a.1, 28.6.0.d.1, 228.6.0.?, 798.6.0.?, 1596.12.0.?	$[(6, 5)]$
22743.d1	22743p2	22743.d	22743p	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{12} \cdot 7 \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$0$	$138240$	$1.947893$	$12246522625/1842183$	$0.89725$	$4.73353$	$[1, -1, 1, -156020, 20444744]$	\(y^2+xy+y=x^3-x^2-156020x+20444744\)	2.3.0.a.1, 28.6.0.a.1, 228.6.0.?, 1596.12.0.?	$[]$
22743.d2	22743p1	22743.d	22743p	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{9} \cdot 7^{2} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$69120$	$1.601318$	$244140625/25137$	$1.08196$	$4.34325$	$[1, -1, 1, -42305, -3026032]$	\(y^2+xy+y=x^3-x^2-42305x-3026032\)	2.3.0.a.1, 28.6.0.b.1, 114.6.0.?, 1596.12.0.?	$[]$
22743.e1	22743i1	22743.e	22743i	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{3} \cdot 7^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$2.134155813$	$1$		$5$	$46080$	$1.226837$	$766060875/931$	$0.86309$	$4.12871$	$[1, -1, 1, -20645, 1145684]$	\(y^2+xy+y=x^3-x^2-20645x+1145684\)	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[(78, 34)]$
22743.e2	22743i2	22743.e	22743i	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{3} \cdot 7^{4} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1.067077906$	$1$		$6$	$92160$	$1.573410$	$-307546875/866761$	$1.04147$	$4.21416$	$[1, -1, 1, -15230, 1756496]$	\(y^2+xy+y=x^3-x^2-15230x+1756496\)	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[(-128, 1327)]$
22743.f1	22743n6	22743.f	22743n	$6$	$8$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{7} \cdot 7^{2} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$6384$	$192$	$1$	$14.77683246$	$1$		$0$	$221184$	$2.095730$	$53297461115137/147$	$1.05087$	$5.56869$	$[1, -1, 1, -2547284, -1564182084]$	\(y^2+xy+y=x^3-x^2-2547284x-1564182084\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$	$[(36422401/120, 154000240141/120)]$
22743.f2	22743n4	22743.f	22743n	$6$	$8$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{8} \cdot 7^{4} \cdot 19^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.18	2Cs	$3192$	$192$	$1$	$7.388416230$	$1$		$2$	$110592$	$1.749157$	$13027640977/21609$	$1.08149$	$4.73969$	$[1, -1, 1, -159269, -24390012]$	\(y^2+xy+y=x^3-x^2-159269x-24390012\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 24.48.0.j.2, $\ldots$	$[(-11119/7, 95985/7)]$
22743.f3	22743n3	22743.f	22743n	$6$	$8$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{14} \cdot 7 \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$6384$	$192$	$1$	$1.847104057$	$1$		$4$	$110592$	$1.749157$	$6570725617/45927$	$1.00160$	$4.67147$	$[1, -1, 1, -126779, 17301156]$	\(y^2+xy+y=x^3-x^2-126779x+17301156\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 48.48.0.bf.1, $\ldots$	$[(-52, 4899)]$
22743.f4	22743n5	22743.f	22743n	$6$	$8$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{7} \cdot 7^{8} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$6384$	$192$	$1$	$3.694208115$	$1$		$0$	$221184$	$2.095730$	$-4354703137/17294403$	$1.04266$	$4.83601$	$[1, -1, 1, -110534, -39634320]$	\(y^2+xy+y=x^3-x^2-110534x-39634320\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$	$[(2015/2, 43467/2)]$
22743.f5	22743n2	22743.f	22743n	$6$	$8$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{10} \cdot 7^{2} \cdot 19^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.10	2Cs	$3192$	$192$	$1$	$3.694208115$	$1$		$4$	$55296$	$1.402584$	$7189057/3969$	$1.14862$	$3.99186$	$[1, -1, 1, -13064, -119982]$	\(y^2+xy+y=x^3-x^2-13064x-119982\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$	$[(-28, 486)]$
22743.f6	22743n1	22743.f	22743n	$6$	$8$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{8} \cdot 7 \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.1	2B	$6384$	$192$	$1$	$7.388416230$	$1$		$1$	$27648$	$1.056011$	$103823/63$	$0.97868$	$3.56945$	$[1, -1, 1, 3181, -16014]$	\(y^2+xy+y=x^3-x^2+3181x-16014\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$	$[(4094/5, 265737/5)]$
22743.g1	22743c2	22743.g	22743c	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{9} \cdot 7^{2} \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$11.23939339$	$1$		$0$	$291840$	$2.223370$	$15438249/49$	$0.87469$	$5.27709$	$[1, -1, 1, -960689, -361192904]$	\(y^2+xy+y=x^3-x^2-960689x-361192904\)	2.3.0.a.1, 28.6.0.d.1, 114.6.0.?, 1596.12.0.?	$[(-807128/37, 10144592/37)]$
22743.g2	22743c1	22743.g	22743c	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{9} \cdot 7 \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$22.47878679$	$1$		$1$	$145920$	$1.876797$	$-729/7$	$0.74333$	$4.57003$	$[1, -1, 1, -34724, -10437362]$	\(y^2+xy+y=x^3-x^2-34724x-10437362\)	2.3.0.a.1, 28.6.0.d.1, 228.6.0.?, 798.6.0.?, 1596.12.0.?	$[(3648856168/3663, 13908442513382/3663)]$
22743.h1	22743j1	22743.h	22743j	$1$	$1$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{3} \cdot 7 \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$84$	$2$	$0$	$1.501495677$	$1$		$2$	$2016$	$-0.367580$	$-13851/7$	$0.67892$	$1.92868$	$[1, -1, 1, -11, -16]$	\(y^2+xy+y=x^3-x^2-11x-16\)	84.2.0.?	$[(6, 7)]$
22743.i1	22743l2	22743.i	22743l	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{12} \cdot 7 \cdot 19^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$4$	$2$	$0$	$729600$	$2.396347$	$6018636259/5103$	$0.93926$	$5.54323$	$[1, -1, 1, -2339348, 1376754234]$	\(y^2+xy+y=x^3-x^2-2339348x+1376754234\)	2.3.0.a.1, 84.6.0.?, 228.6.0.?, 266.6.0.?, 1596.12.0.?	$[]$
22743.i2	22743l1	22743.i	22743l	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{9} \cdot 7^{2} \cdot 19^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$4$	$2$	$1$	$364800$	$2.049770$	$2685619/1323$	$0.89213$	$4.77422$	$[1, -1, 1, -178763, 11264514]$	\(y^2+xy+y=x^3-x^2-178763x+11264514\)	2.3.0.a.1, 84.6.0.?, 114.6.0.?, 532.6.0.?, 1596.12.0.?	$[]$
22743.j1	22743h1	22743.j	22743h	$1$	$1$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{9} \cdot 7 \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$84$	$2$	$0$	$1.132229902$	$1$		$2$	$6048$	$0.181726$	$-13851/7$	$0.67892$	$2.58574$	$[1, -1, 0, -96, 521]$	\(y^2+xy=x^3-x^2-96x+521\)	84.2.0.?	$[(-8, 31)]$
22743.k1	22743b2	22743.k	22743b	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{3} \cdot 7^{2} \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$4.017322314$	$1$		$4$	$97280$	$1.674065$	$15438249/49$	$0.87469$	$4.62002$	$[1, -1, 0, -106743, 13413096]$	\(y^2+xy=x^3-x^2-106743x+13413096\)	2.3.0.a.1, 28.6.0.d.1, 114.6.0.?, 1596.12.0.?	$[(180, -6)]$
22743.k2	22743b1	22743.k	22743b	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{3} \cdot 7 \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$8.034644628$	$1$		$3$	$48640$	$1.327492$	$-729/7$	$0.74333$	$3.91297$	$[1, -1, 0, -3858, 387855]$	\(y^2+xy=x^3-x^2-3858x+387855\)	2.3.0.a.1, 28.6.0.d.1, 228.6.0.?, 798.6.0.?, 1596.12.0.?	$[(3046, 166533)]$
22743.l1	22743m2	22743.l	22743m	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{16} \cdot 7^{3} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$8.900255157$	$1$		$0$	$691200$	$2.735806$	$789529529265625/7311624327$	$1.01939$	$5.83739$	$[1, -1, 0, -6256017, 5975932410]$	\(y^2+xy=x^3-x^2-6256017x+5975932410\)	2.3.0.a.1, 28.6.0.a.1, 228.6.0.?, 1596.12.0.?	$[(842011/22, 191459655/22)]$
22743.l2	22743m1	22743.l	22743m	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{11} \cdot 7^{6} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$4.450127578$	$1$		$1$	$345600$	$2.389233$	$1031831907625/543185433$	$0.96952$	$5.17550$	$[1, -1, 0, -683982, -65267937]$	\(y^2+xy=x^3-x^2-683982x-65267937\)	2.3.0.a.1, 28.6.0.b.1, 114.6.0.?, 1596.12.0.?	$[(-797/2, 64333/2)]$
22743.m1	22743g1	22743.m	22743g	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{9} \cdot 7^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$14.43776044$	$1$		$1$	$138240$	$1.776142$	$766060875/931$	$0.86309$	$4.78577$	$[1, -1, 0, -185802, -30747673]$	\(y^2+xy=x^3-x^2-185802x-30747673\)	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[(74859854/275, 560977078383/275)]$
22743.m2	22743g2	22743.m	22743g	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{9} \cdot 7^{4} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$7.218880223$	$1$		$0$	$276480$	$2.122715$	$-307546875/866761$	$1.04147$	$4.87122$	$[1, -1, 0, -137067, -47288332]$	\(y^2+xy=x^3-x^2-137067x-47288332\)	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[(79436/11, 15609552/11)]$
22743.n1	22743a2	22743.n	22743a	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{9} \cdot 7^{2} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$2.601886829$	$1$		$2$	$15360$	$0.751151$	$15438249/49$	$0.87469$	$3.51606$	$[1, -1, 0, -2661, 53360]$	\(y^2+xy=x^3-x^2-2661x+53360\)	2.3.0.a.1, 28.6.0.d.1, 114.6.0.?, 1596.12.0.?	$[(-32, 340)]$
22743.n2	22743a1	22743.n	22743a	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{9} \cdot 7 \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$5.203773659$	$1$		$1$	$7680$	$0.404578$	$-729/7$	$0.74333$	$2.80901$	$[1, -1, 0, -96, 1547]$	\(y^2+xy=x^3-x^2-96x+1547\)	2.3.0.a.1, 28.6.0.d.1, 228.6.0.?, 798.6.0.?, 1596.12.0.?	$[(-62/3, 1253/3)]$
22743.o1	22743e1	22743.o	22743e	$1$	$1$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 3^{3} \cdot 7 \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$84$	$2$	$0$	$1$	$1$		$0$	$38304$	$1.104639$	$-13851/7$	$0.67892$	$3.68970$	$[1, -1, 0, -3858, 127213]$	\(y^2+xy=x^3-x^2-3858x+127213\)	84.2.0.?	$[]$
22743.p1	22743k2	22743.p	22743k	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{12} \cdot 7 \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$4$	$2$	$0$	$38400$	$0.924127$	$6018636259/5103$	$0.93926$	$3.78220$	$[1, -1, 0, -6480, -199017]$	\(y^2+xy=x^3-x^2-6480x-199017\)	2.3.0.a.1, 84.6.0.?, 228.6.0.?, 266.6.0.?, 1596.12.0.?	$[]$
22743.p2	22743k1	22743.p	22743k	$2$	$2$	\( 3^{2} \cdot 7 \cdot 19^{2} \)	\( 3^{9} \cdot 7^{2} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$19200$	$0.577553$	$2685619/1323$	$0.89213$	$3.01320$	$[1, -1, 0, -495, -1512]$	\(y^2+xy=x^3-x^2-495x-1512\)	2.3.0.a.1, 84.6.0.?, 114.6.0.?, 532.6.0.?, 1596.12.0.?	$[]$