LMFDB - Elliptic curves over $\Q$ of conductor 16016

Refine search

Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

		Sort order	Select

Results (27 matches)

Download displayed columns for results to

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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
16016.a1	16016c1	16016.a	16016c	$1$	$1$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 7^{2} \cdot 11^{5} \cdot 13^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$0.185451843$	$1$		$4$	$119040$	$1.751728$	$14622648823378944/38090758396691$	$0.99083$	$4.54685$	$[0, 0, 0, 32348, 4190188]$	$y^2=x^3+32348x+4190188$	22.2.0.a.1	$[(529, 13013)]$
16016.b1	16016l1	16016.b	16016l	$1$	$1$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{12} \cdot 7^{3} \cdot 11^{4} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1$	$1$		$0$	$120960$	$1.902390$	$-442980486619070464/1864582578859$	$1.00426$	$5.05687$	$[0, 1, 0, -254101, -49564989]$	$y^2=x^3+x^2-254101x-49564989$	182.2.0.?	$[]$
16016.c1	16016f1	16016.c	16016f	$2$	$2$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{4} \cdot 7 \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4004$	$12$	$0$	$1$	$1$		$1$	$3360$	$-0.262504$	$67108864/13013$	$0.89856$	$2.14789$	$[0, 1, 0, -21, -38]$	$y^2=x^3+x^2-21x-38$	2.3.0.a.1, 52.6.0.b.1, 154.6.0.?, 4004.12.0.?	$[]$
16016.c2	16016f2	16016.c	16016f	$2$	$2$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 7^{2} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4004$	$12$	$0$	$1$	$1$		$1$	$6720$	$0.084069$	$35969456/77077$	$0.74511$	$2.47256$	$[0, 1, 0, 44, -168]$	$y^2=x^3+x^2+44x-168$	2.3.0.a.1, 52.6.0.a.1, 308.6.0.?, 4004.12.0.?	$[]$
16016.d1	16016a2	16016.d	16016a	$2$	$2$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 7 \cdot 11^{2} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$8008$	$12$	$0$	$0.532103490$	$1$		$9$	$3328$	$0.345743$	$853915554/143143$	$0.84588$	$2.91178$	$[0, 0, 0, -251, 1290]$	$y^2=x^3-251x+1290$	2.3.0.a.1, 56.6.0.a.1, 572.6.0.?, 8008.12.0.?	$[(-7, 52)]$
16016.d2	16016a1	16016.d	16016a	$2$	$2$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{10} \cdot 7^{2} \cdot 11 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$8008$	$12$	$0$	$1.064206980$	$1$		$5$	$1664$	$-0.000830$	$2634012/7007$	$0.77452$	$2.37524$	$[0, 0, 0, 29, 114]$	$y^2=x^3+29x+114$	2.3.0.a.1, 56.6.0.d.1, 286.6.0.?, 8008.12.0.?	$[(1, 12)]$
16016.e1	16016j4	16016.e	16016j	$4$	$4$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{12} \cdot 7^{4} \cdot 11 \cdot 13^{2} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$616$	$48$	$0$	$4.239088487$	$1$		$5$	$38912$	$1.455376$	$107818231938348177/4463459$	$0.97120$	$4.91016$	$[0, 0, 0, -158651, 24322730]$	$y^2=x^3-158651x+24322730$	2.3.0.a.1, 4.12.0-4.c.1.1, 44.24.0-44.h.1.2, 56.24.0-56.z.1.4, 616.48.0.?	$[(311, 2250)]$
16016.e2	16016j3	16016.e	16016j	$4$	$4$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{12} \cdot 7 \cdot 11 \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$616$	$48$	$0$	$4.239088487$	$1$		$3$	$38912$	$1.455376$	$112489728522417/62811265517$	$0.98191$	$4.20103$	$[0, 0, 0, -16091, -147254]$	$y^2=x^3-16091x-147254$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 28.12.0-4.c.1.2, 44.12.0-4.c.1.2, $\ldots$	$[(-41, 666)]$
16016.e3	16016j2	16016.e	16016j	$4$	$4$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{12} \cdot 7^{2} \cdot 11^{2} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$308$	$48$	$0$	$2.119544243$	$1$		$9$	$19456$	$1.108801$	$26444947540257/169338169$	$1.03178$	$4.05149$	$[0, 0, 0, -9931, 378810]$	$y^2=x^3-9931x+378810$	2.6.0.a.1, 4.12.0-2.a.1.1, 28.24.0-28.b.1.2, 44.24.0-44.a.1.1, 308.48.0.?	$[(47, 126)]$
16016.e4	16016j1	16016.e	16016j	$4$	$4$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{12} \cdot 7 \cdot 11^{4} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$616$	$48$	$0$	$1.059772121$	$1$		$7$	$9728$	$0.762228$	$-426957777/17320303$	$1.05776$	$3.35222$	$[0, 0, 0, -251, 12906]$	$y^2=x^3-251x+12906$	2.3.0.a.1, 4.12.0-4.c.1.2, 14.6.0.b.1, 28.24.0-28.g.1.1, 88.24.0.?, $\ldots$	$[(-19, 104)]$
16016.f1	16016g3	16016.f	16016g	$4$	$4$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{14} \cdot 7 \cdot 11 \cdot 13^{4} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$8008$	$48$	$0$	$4.931640385$	$1$		$5$	$18432$	$1.152775$	$493357359497913/8796788$	$0.93959$	$4.35374$	$[0, 0, 0, -26339, 1645282]$	$y^2=x^3-26339x+1645282$	2.3.0.a.1, 4.12.0-4.c.1.1, 104.24.0.?, 154.6.0.?, 308.24.0.?, $\ldots$	$[(319, 5070)]$
16016.f2	16016g2	16016.f	16016g	$4$	$4$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{16} \cdot 7^{2} \cdot 11^{2} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$4004$	$48$	$0$	$2.465820192$	$1$		$7$	$9216$	$0.806201$	$132417047673/16032016$	$0.91332$	$3.50437$	$[0, 0, 0, -1699, 23970]$	$y^2=x^3-1699x+23970$	2.6.0.a.1, 4.12.0-2.a.1.1, 52.24.0-52.a.1.2, 308.24.0.?, 4004.48.0.?	$[(-33, 210)]$
16016.f3	16016g1	16016.f	16016g	$4$	$4$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{20} \cdot 7 \cdot 11 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$8008$	$48$	$0$	$4.931640385$	$1$		$1$	$4608$	$0.459628$	$1986121593/256256$	$0.86575$	$3.07057$	$[0, 0, 0, -419, -2910]$	$y^2=x^3-419x-2910$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 52.12.0-4.c.1.1, 104.24.0.?, $\ldots$	$[(-110/3, 530/3)]$
16016.f4	16016g4	16016.f	16016g	$4$	$4$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{14} \cdot 7^{4} \cdot 11^{4} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$8008$	$48$	$0$	$4.931640385$	$1$		$1$	$18432$	$1.152775$	$402437650887/1827958132$	$0.92555$	$3.81793$	$[0, 0, 0, 2461, 122978]$	$y^2=x^3+2461x+122978$	2.3.0.a.1, 4.12.0-4.c.1.2, 52.24.0-52.h.1.1, 616.24.0.?, 8008.48.0.?	$[(2719/3, 143990/3)]$
16016.g1	16016m2	16016.g	16016m	$2$	$2$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{21} \cdot 7 \cdot 11^{2} \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$8008$	$12$	$0$	$1.121126483$	$1$		$3$	$103680$	$1.927486$	$712928482228623753/2093213298176$	$1.02331$	$5.10528$	$[0, 0, 0, -297779, 62385650]$	$y^2=x^3-297779x+62385650$	2.3.0.a.1, 56.6.0.a.1, 572.6.0.?, 8008.12.0.?	$[(-23, 8320)]$
16016.g2	16016m1	16016.g	16016m	$2$	$2$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{30} \cdot 7^{2} \cdot 11 \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$8008$	$12$	$0$	$2.242252966$	$1$		$3$	$51840$	$1.580912$	$-36518366116233/310426468352$	$1.00255$	$4.36918$	$[0, 0, 0, -11059, 1773042]$	$y^2=x^3-11059x+1773042$	2.3.0.a.1, 56.6.0.d.1, 286.6.0.?, 8008.12.0.?	$[(199, 2730)]$
16016.h1	16016h2	16016.h	16016h	$2$	$2$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{13} \cdot 7^{2} \cdot 11 \cdot 13^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$19968$	$0.831480$	$88061730849/30788758$	$0.92252$	$3.46223$	$[0, 0, 0, -1483, -13830]$	$y^2=x^3-1483x-13830$	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[]$
16016.h2	16016h1	16016.h	16016h	$2$	$2$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{14} \cdot 7 \cdot 11^{2} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$9984$	$0.484906$	$573856191/572572$	$0.83130$	$2.94232$	$[0, 0, 0, 277, -1510]$	$y^2=x^3+277x-1510$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[]$
16016.i1	16016d1	16016.i	16016d	$1$	$1$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 7^{2} \cdot 11 \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1.115984331$	$1$		$2$	$2816$	$0.094187$	$5030912/91091$	$0.77962$	$2.51897$	$[0, 1, 0, 23, -221]$	$y^2=x^3+x^2+23x-221$	22.2.0.a.1	$[(6, 13)]$
16016.j1	16016n1	16016.j	16016n	$1$	$1$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 7^{6} \cdot 11 \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$0.177631543$	$1$		$4$	$12672$	$0.846499$	$-8667872124928/218709491$	$0.90199$	$3.65430$	$[0, 1, 0, -2717, 54791]$	$y^2=x^3+x^2-2717x+54791$	22.2.0.a.1	$[(47, 182)]$
16016.k1	16016b1	16016.k	16016b	$1$	$1$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 7 \cdot 11^{8} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1$	$1$		$0$	$705024$	$2.710777$	$-21203116761178214318777344/3296625230899$	$1.02362$	$6.59633$	$[0, -1, 0, -36613281, 85284134429]$	$y^2=x^3-x^2-36613281x+85284134429$	182.2.0.?	$[]$
16016.l1	16016i3	16016.l	16016i	$4$	$6$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{4} \cdot 7 \cdot 11^{3} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$12012$	$96$	$1$	$1$	$1$		$1$	$16416$	$0.968605$	$92401696768000/44971379453$	$1.00430$	$3.60795$	$[0, -1, 0, -2373, 18536]$	$y^2=x^3-x^2-2373x+18536$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.9, 52.6.0.b.1, $\ldots$	$[]$
16016.l2	16016i1	16016.l	16016i	$4$	$6$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ 2^{4} \cdot 7^{3} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$12012$	$96$	$1$	$1$	$9$	$3$	$1$	$5472$	$0.419299$	$13608288256000/637637$	$0.95888$	$3.41009$	$[0, -1, 0, -1253, -16660]$	$y^2=x^3-x^2-1253x-16660$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.3, 52.6.0.b.1, $\ldots$	$[]$
16016.l3	16016i2	16016.l	16016i	$4$	$6$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 7^{6} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$12012$	$96$	$1$	$1$	$9$	$3$	$1$	$10944$	$0.765873$	$-724934194000/185061877$	$0.84902$	$3.43134$	$[0, -1, 0, -1188, -18532]$	$y^2=x^3-x^2-1188x-18532$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.3, 52.6.0.a.1, $\ldots$	$[]$
16016.l4	16016i4	16016.l	16016i	$4$	$6$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 7^{2} \cdot 11^{6} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$12012$	$96$	$1$	$1$	$1$		$1$	$32832$	$1.315178$	$275895984926000/190713856333$	$0.92114$	$4.00732$	$[0, -1, 0, 8612, 132780]$	$y^2=x^3-x^2+8612x+132780$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.9, 52.6.0.a.1, $\ldots$	$[]$
16016.m1	16016e1	16016.m	16016e	$1$	$1$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{8} \cdot 7 \cdot 11^{4} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$182$	$2$	$0$	$1$	$1$		$0$	$5888$	$0.326768$	$2302045184/1332331$	$0.98556$	$2.79943$	$[0, -1, 0, 175, -67]$	$y^2=x^3-x^2+175x-67$	182.2.0.?	$[]$
16016.n1	16016k1	16016.n	16016k	$1$	$1$	$ 2^{4} \cdot 7 \cdot 11 \cdot 13 $	$ - 2^{12} \cdot 7^{2} \cdot 11^{3} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$5.616128946$	$1$		$0$	$40320$	$0.854242$	$-871531204608/11022011$	$0.89651$	$3.70123$	$[0, 0, 0, -3184, -69904]$	$y^2=x^3-3184x-69904$	22.2.0.a.1	$[(697/3, 10387/3)]$

Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (27 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Learn more

Refine search Advanced search options

Results (27 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Refine search