Elliptic curves over Q\Q of conductor 16245

Results (32 matches)

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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
16245.a1	16245n1	16245.a	16245n	$1$	$1$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{20} \cdot 5^{3} \cdot 19^{10}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1$	$1$		$0$	$3217536$	$3.391376$	$1914902401024/597871125$	$1.06216$	$6.63364$	$[0, 0, 1, -42614967, 72660506130]$	$y^2+y=x^3-42614967x+72660506130$	10.2.0.a.1	$[]$
16245.b1	16245i1	16245.b	16245i	$1$	$1$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{8} \cdot 5 \cdot 19^{8}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1.044960297$	$1$		$4$	$109440$	$1.518972$	$77824/45$	$1.11940$	$4.27097$	$[0, 0, 1, -20577, 32580]$	$y^2+y=x^3-20577x+32580$	10.2.0.a.1	$[(0, 180)]$
16245.c1	16245d7	16245.c	16245d	$8$	$16$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{10} \cdot 5 \cdot 19^{6}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.121	2B	$9120$	$768$	$13$	$16.44430019$	$1$		$0$	$221184$	$2.312397$	$1114544804970241/405$	$1.07354$	$6.07553$	$[1, -1, 1, -7017908, -7154068534]$	$y^2+xy+y=x^3-x^2-7017908x-7154068534$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$	$[(241989799/118, 3703451766397/118)]$
16245.c2	16245d5	16245.c	16245d	$8$	$16$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{14} \cdot 5^{2} \cdot 19^{6}$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.123	2Cs	$4560$	$768$	$13$	$8.222150098$	$1$		$2$	$110592$	$1.965822$	$272223782641/164025$	$1.03897$	$5.21768$	$[1, -1, 1, -438683, -111666094]$	$y^2+xy+y=x^3-x^2-438683x-111666094$	2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$	$[(69199/2, 18120143/2)]$
16245.c3	16245d8	16245.c	16245d	$8$	$16$	$3^{2} \cdot 5 \cdot 19^{2}$	$- 3^{22} \cdot 5 \cdot 19^{6}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.134	2B	$9120$	$768$	$13$	$16.44430019$	$1$		$0$	$221184$	$2.312397$	$-147281603041/215233605$	$1.05949$	$5.28427$	$[1, -1, 1, -357458, -154357954]$	$y^2+xy+y=x^3-x^2-357458x-154357954$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$	$[(257475799/122, 4113143706683/122)]$
16245.c4	16245d4	16245.c	16245d	$8$	$16$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{7} \cdot 5 \cdot 19^{6}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$9120$	$768$	$13$	$4.111075049$	$1$		$0$	$55296$	$1.619247$	$56667352321/15$	$1.03019$	$5.05581$	$[1, -1, 1, -259988, 51089312]$	$y^2+xy+y=x^3-x^2-259988x+51089312$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$	$[(1215/2, 959/2)]$
16245.c5	16245d3	16245.c	16245d	$8$	$16$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{10} \cdot 5^{4} \cdot 19^{6}$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.44	2Cs	$4560$	$768$	$13$	$4.111075049$	$1$		$4$	$55296$	$1.619247$	$111284641/50625$	$1.02534$	$4.41295$	$[1, -1, 1, -32558, -1037644]$	$y^2+xy+y=x^3-x^2-32558x-1037644$	2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$	$[(799/2, 4251/2)]$
16245.c6	16245d2	16245.c	16245d	$8$	$16$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{8} \cdot 5^{2} \cdot 19^{6}$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.3	2Cs	$4560$	$768$	$13$	$2.055537524$	$1$		$6$	$27648$	$1.272675$	$13997521/225$	$0.96230$	$4.19912$	$[1, -1, 1, -16313, 794792]$	$y^2+xy+y=x^3-x^2-16313x+794792$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$	$[(33, 523)]$
16245.c7	16245d1	16245.c	16245d	$8$	$16$	$3^{2} \cdot 5 \cdot 19^{2}$	$- 3^{7} \cdot 5 \cdot 19^{6}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$9120$	$768$	$13$	$1.027768762$	$1$		$7$	$13824$	$0.926101$	$-1/15$	$1.19808$	$3.55020$	$[1, -1, 1, -68, 34526]$	$y^2+xy+y=x^3-x^2-68x+34526$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$	$[(-14, 187)]$
16245.c8	16245d6	16245.c	16245d	$8$	$16$	$3^{2} \cdot 5 \cdot 19^{2}$	$- 3^{8} \cdot 5^{8} \cdot 19^{6}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.197	2B	$9120$	$768$	$13$	$8.222150098$	$1$		$0$	$110592$	$1.965822$	$4733169839/3515625$	$1.05585$	$4.79975$	$[1, -1, 1, 113647, -7880038]$	$y^2+xy+y=x^3-x^2+113647x-7880038$	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$	$[(14527/14, 2566173/14)]$
16245.d1	16245l2	16245.d	16245l	$2$	$2$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{16} \cdot 5^{2} \cdot 19^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$0$	$230400$	$2.140167$	$48587168449/28048275$	$1.03180$	$5.03994$	$[1, -1, 1, -246992, -2283816]$	$y^2+xy+y=x^3-x^2-246992x-2283816$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.?	$[]$
16245.d2	16245l1	16245.d	16245l	$2$	$2$	$3^{2} \cdot 5 \cdot 19^{2}$	$- 3^{11} \cdot 5 \cdot 19^{8}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$4$	$2$	$1$	$115200$	$1.793594$	$756058031/438615$	$1.00322$	$4.61057$	$[1, -1, 1, 61663, -308424]$	$y^2+xy+y=x^3-x^2+61663x-308424$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[]$
16245.e1	16245g2	16245.e	16245g	$2$	$2$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{10} \cdot 5^{2} \cdot 19^{3}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$0.966889388$	$1$		$6$	$10240$	$0.633922$	$9393931/2025$	$0.89098$	$3.24691$	$[1, -1, 1, -752, -6096]$	$y^2+xy+y=x^3-x^2-752x-6096$	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 380.12.0.?	$[(-16, 48)]$
16245.e2	16245g1	16245.e	16245g	$2$	$2$	$3^{2} \cdot 5 \cdot 19^{2}$	$- 3^{8} \cdot 5 \cdot 19^{3}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1.933778777$	$1$		$5$	$5120$	$0.287348$	$24389/45$	$0.82301$	$2.71362$	$[1, -1, 1, 103, -624]$	$y^2+xy+y=x^3-x^2+103x-624$	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 190.6.0.?, 380.12.0.?	$[(14, 51)]$
16245.f1	16245a2	16245.f	16245a	$2$	$3$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{8} \cdot 5 \cdot 19^{8}$	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$1$	$9$	$3$	$2$	$590976$	$2.790077$	$1590409933520896/45$	$1.29281$	$6.71958$	$[0, 0, 1, -56257518, 162412318188]$	$y^2+y=x^3-56257518x+162412318188$	3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4	$[]$
16245.f2	16245a1	16245.f	16245a	$2$	$3$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{12} \cdot 5^{3} \cdot 19^{8}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$1$	$1$		$0$	$196992$	$2.240772$	$3058794496/91125$	$0.98270$	$5.36210$	$[0, 0, 1, -699618, 219362823]$	$y^2+y=x^3-699618x+219362823$	3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1	$[]$
16245.g1	16245b2	16245.g	16245b	$2$	$3$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{8} \cdot 5 \cdot 19^{2}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$570$	$16$	$0$	$9.284794529$	$1$		$0$	$31104$	$1.317858$	$1590409933520896/45$	$1.29281$	$4.89744$	$[0, 0, 1, -155838, -23678717]$	$y^2+y=x^3-155838x-23678717$	3.4.0.a.1, 10.2.0.a.1, 30.8.0.a.1, 57.8.0-3.a.1.1, 570.16.0.?	$[(-2188903/98, -464591/98)]$
16245.g2	16245b1	16245.g	16245b	$2$	$3$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{12} \cdot 5^{3} \cdot 19^{2}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$570$	$16$	$0$	$3.094931509$	$1$		$2$	$10368$	$0.768552$	$3058794496/91125$	$0.98270$	$3.53996$	$[0, 0, 1, -1938, -31982]$	$y^2+y=x^3-1938x-31982$	3.4.0.a.1, 10.2.0.a.1, 30.8.0.a.1, 57.8.0-3.a.1.2, 570.16.0.?	$[(-22, 2)]$
16245.h1	16245j2	16245.h	16245j	$2$	$3$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{6} \cdot 5^{9} \cdot 19^{2}$	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.2	3B	$1710$	$144$	$2$	$0.465110768$	$1$		$12$	$18144$	$0.956387$	$7575076864/1953125$	$1.00586$	$3.63349$	$[0, 0, 1, -2622, -38480]$	$y^2+y=x^3-2622x-38480$	3.4.0.a.1, 9.12.0.b.1, 10.2.0.a.1, 30.8.0.a.1, 57.8.0-3.a.1.1, $\ldots$	$[(-32, 112), (58, 67)]$
16245.h2	16245j1	16245.h	16245j	$2$	$3$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{6} \cdot 5^{3} \cdot 19^{2}$	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.2	3B	$1710$	$144$	$2$	$0.465110768$	$1$		$14$	$6048$	$0.407080$	$318767104/125$	$1.09713$	$3.30673$	$[0, 0, 1, -912, 10597]$	$y^2+y=x^3-912x+10597$	3.4.0.a.1, 9.12.0.b.1, 10.2.0.a.1, 30.8.0.a.1, 57.8.0-3.a.1.2, $\ldots$	$[(17, 2), (7, 67)]$
16245.i1	16245e2	16245.i	16245e	$2$	$3$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{6} \cdot 5^{9} \cdot 19^{8}$	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.2	3B.1.1	$1710$	$144$	$2$	$2.586444006$	$1$		$6$	$344736$	$2.428604$	$7575076864/1953125$	$1.00586$	$5.45563$	$[0, 0, 1, -946542, 263932605]$	$y^2+y=x^3-946542x+263932605$	3.8.0-3.a.1.2, 9.24.0-9.b.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4, 90.48.0.?, $\ldots$	$[(833, 7312)]$
16245.i2	16245e1	16245.i	16245e	$2$	$3$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{6} \cdot 5^{3} \cdot 19^{8}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.4	3B.1.2	$1710$	$144$	$2$	$0.862148002$	$1$		$4$	$114912$	$1.879299$	$318767104/125$	$1.09713$	$5.12887$	$[0, 0, 1, -329232, -72686538]$	$y^2+y=x^3-329232x-72686538$	3.8.0-3.a.1.1, 9.24.0-9.b.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1, 90.48.0.?, $\ldots$	$[(722, 8122)]$
16245.j1	16245c3	16245.j	16245c	$4$	$4$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{8} \cdot 5^{3} \cdot 19^{10}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2280$	$48$	$0$	$39.39376491$	$1$		$0$	$829440$	$2.775665$	$23977812996389881/146611125$	$1.09826$	$6.39203$	$[1, -1, 0, -19518435, -33185583684]$	$y^2+xy=x^3-x^2-19518435x-33185583684$	2.3.0.a.1, 4.6.0.c.1, 10.6.0.a.1, 20.12.0.g.1, 24.12.0-4.c.1.3, $\ldots$	$[(-3631521783781244895/37719248, 88868122687073948516744937/37719248)]$
16245.j2	16245c4	16245.j	16245c	$4$	$4$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{8} \cdot 5^{12} \cdot 19^{7}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2280$	$48$	$0$	$9.848441229$	$1$		$0$	$829440$	$2.775665$	$209595169258201/41748046875$	$0.98100$	$5.90318$	$[1, -1, 0, -4020705, 2513992950]$	$y^2+xy=x^3-x^2-4020705x+2513992950$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.z.1, 76.12.0.?, $\ldots$	$[(5202/7, 15656292/7)]$
16245.j3	16245c2	16245.j	16245c	$4$	$4$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{10} \cdot 5^{6} \cdot 19^{8}$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1140$	$48$	$0$	$19.69688245$	$1$		$2$	$414720$	$2.429092$	$6189976379881/456890625$	$0.95560$	$5.53989$	$[1, -1, 0, -1242810, -497800809]$	$y^2+xy=x^3-x^2-1242810x-497800809$	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.b.1, 60.24.0-20.b.1.3, 76.12.0.?, $\ldots$	$[(-2415902130/2149, 32338290966381/2149)]$
16245.j4	16245c1	16245.j	16245c	$4$	$4$	$3^{2} \cdot 5 \cdot 19^{2}$	$- 3^{14} \cdot 5^{3} \cdot 19^{7}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2280$	$48$	$0$	$9.848441229$	$1$		$1$	$207360$	$2.082516$	$1256216039/15582375$	$0.94875$	$4.97413$	$[1, -1, 0, 73035, -34360200]$	$y^2+xy=x^3-x^2+73035x-34360200$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.z.1, 120.24.0.?, $\ldots$	$[(524968/31, 378375588/31)]$
16245.k1	16245k2	16245.k	16245k	$2$	$2$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{8} \cdot 5^{6} \cdot 19^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$0$	$138240$	$2.031864$	$90458382169/2671875$	$1.09032$	$5.10404$	$[1, -1, 0, -303849, -62723970]$	$y^2+xy=x^3-x^2-303849x-62723970$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.?	$[]$
16245.k2	16245k1	16245.k	16245k	$2$	$2$	$3^{2} \cdot 5 \cdot 19^{2}$	$- 3^{7} \cdot 5^{3} \cdot 19^{8}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$1$	$69120$	$1.685291$	$357911/135375$	$0.95197$	$4.48941$	$[1, -1, 0, 4806, -3277017]$	$y^2+xy=x^3-x^2+4806x-3277017$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[]$
16245.l1	16245f2	16245.l	16245f	$2$	$2$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{10} \cdot 5^{2} \cdot 19^{9}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$6.235771154$	$1$		$0$	$194560$	$2.106140$	$9393931/2025$	$0.89098$	$5.06905$	$[1, -1, 0, -271359, 43167438]$	$y^2+xy=x^3-x^2-271359x+43167438$	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 380.12.0.?	$[(-2217/2, 40647/2)]$
16245.l2	16245f1	16245.l	16245f	$2$	$2$	$3^{2} \cdot 5 \cdot 19^{2}$	$- 3^{8} \cdot 5 \cdot 19^{9}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$12.47154230$	$1$		$1$	$97280$	$1.759567$	$24389/45$	$0.82301$	$4.53576$	$[1, -1, 0, 37296, 4091715]$	$y^2+xy=x^3-x^2+37296x+4091715$	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 190.6.0.?, 380.12.0.?	$[(-248751/56, 146307267/56)]$
16245.m1	16245h1	16245.m	16245h	$1$	$1$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{20} \cdot 5^{3} \cdot 19^{4}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$6.139490043$	$1$		$0$	$169344$	$1.919157$	$1914902401024/597871125$	$1.06216$	$4.81150$	$[0, 0, 1, -118047, -10593455]$	$y^2+y=x^3-118047x-10593455$	10.2.0.a.1	$[(-943/2, 16261/2)]$
16245.n1	16245m1	16245.n	16245m	$1$	$1$	$3^{2} \cdot 5 \cdot 19^{2}$	$3^{8} \cdot 5 \cdot 19^{2}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1$	$1$		$0$	$5760$	$0.046754$	$77824/45$	$1.11940$	$2.44883$	$[0, 0, 1, -57, -5]$	$y^2+y=x^3-57x-5$	10.2.0.a.1	$[]$

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