LMFDB - Elliptic curves over $\Q$ of conductor 56144

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	Manin constant

		Sort order	Select

Results (28 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
56144.a1	56144n1	56144.a	56144n	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{12} \cdot 11^{8} \cdot 29^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$58$	$2$	$0$	$2.896284134$	$1$		$2$	$696960$	$2.135986$	$131753070592/24389$	$1.02883$	$4.85614$	$[0, 1, 0, -1015109, 393255091]$	$y^2=x^3+x^2-1015109x+393255091$	58.2.0.a.1	$[(766, 8107)]$
56144.b1	56144t1	56144.b	56144t	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{12} \cdot 11^{2} \cdot 29^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$58$	$2$	$0$	$4.167065087$	$1$		$4$	$63360$	$0.937039$	$131753070592/24389$	$1.02883$	$3.54050$	$[0, 1, 0, -8389, -298509]$	$y^2=x^3+x^2-8389x-298509$	58.2.0.a.1	$[(-211/2, 29/2), (-482/3, 145/3)]$
56144.c1	56144u1	56144.c	56144u	$2$	$2$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{4} \cdot 11^{6} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$2552$	$48$	$0$	$1$	$1$		$1$	$32400$	$0.556383$	$5619712/29$	$0.88985$	$2.99037$	$[0, 1, 0, -1129, 14166]$	$y^2=x^3+x^2-1129x+14166$	2.3.0.a.1, 4.6.0.b.1, 58.6.0.a.1, 88.12.0.?, 116.24.0.?, $\ldots$	$[ ]$
56144.c2	56144u2	56144.c	56144u	$2$	$2$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{8} \cdot 11^{6} \cdot 29^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$2552$	$48$	$0$	$1$	$1$		$1$	$64800$	$0.902957$	$-35152/841$	$0.85096$	$3.12242$	$[0, 1, 0, -524, 29896]$	$y^2=x^3+x^2-524x+29896$	2.3.0.a.1, 4.6.0.a.1, 88.12.0.?, 116.12.0.?, 232.24.0.?, $\ldots$	$[ ]$
56144.d1	56144g1	56144.d	56144g	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{10} \cdot 11^{6} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$116$	$2$	$0$	$11.23434409$	$1$		$0$	$43200$	$1.008217$	$-55990084/29$	$0.87197$	$3.58098$	$[0, -1, 0, -9720, -365792]$	$y^2=x^3-x^2-9720x-365792$	116.2.0.?	$[(150862/3, 58593482/3)]$
56144.e1	56144r1	56144.e	56144r	$2$	$3$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{8} \cdot 11^{6} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3828$	$16$	$0$	$1$	$1$		$0$	$43200$	$0.639628$	$-35152/29$	$0.71422$	$2.86092$	$[0, -1, 0, -524, 7372]$	$y^2=x^3-x^2-524x+7372$	3.4.0.a.1, 116.2.0.?, 132.8.0.?, 348.8.0.?, 1914.8.0.?, $\ldots$	$[ ]$
56144.e2	56144r2	56144.e	56144r	$2$	$3$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{8} \cdot 11^{6} \cdot 29^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3828$	$16$	$0$	$1$	$1$		$0$	$129600$	$1.188934$	$19600688/24389$	$0.87422$	$3.37094$	$[0, -1, 0, 4316, -118468]$	$y^2=x^3-x^2+4316x-118468$	3.4.0.a.1, 116.2.0.?, 132.8.0.?, 348.8.0.?, 1914.8.0.?, $\ldots$	$[ ]$
56144.f1	56144j2	56144.f	56144j	$2$	$2$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{13} \cdot 11^{9} \cdot 29^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2552$	$12$	$0$	$2.055553872$	$1$		$5$	$418176$	$1.913208$	$112678587/1682$	$1.00269$	$4.42944$	$[0, 0, 0, -214291, -37685934]$	$y^2=x^3-214291x-37685934$	2.3.0.a.1, 88.6.0.?, 232.6.0.?, 1276.6.0.?, 2552.12.0.?	$[(-271, 696)]$
56144.f2	56144j1	56144.f	56144j	$2$	$2$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{14} \cdot 11^{9} \cdot 29 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2552$	$12$	$0$	$4.111107745$	$1$		$3$	$209088$	$1.566635$	$-27/116$	$0.97231$	$3.85045$	$[0, 0, 0, -1331, -1610510]$	$y^2=x^3-1331x-1610510$	2.3.0.a.1, 88.6.0.?, 232.6.0.?, 638.6.0.?, 2552.12.0.?	$[(265, 4080)]$
56144.g1	56144d1	56144.g	56144d	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{8} \cdot 11^{2} \cdot 29^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$58$	$2$	$0$	$0.714770462$	$1$		$2$	$57600$	$0.954469$	$35780355072/20511149$	$1.20798$	$3.16776$	$[0, 0, 0, -2156, 3740]$	$y^2=x^3-2156x+3740$	58.2.0.a.1	$[(97, 841)]$
56144.h1	56144p1	56144.h	56144p	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{12} \cdot 11^{8} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$58$	$2$	$0$	$1$	$4$	$2$	$0$	$105600$	$1.357317$	$1216512/29$	$0.71531$	$3.79606$	$[0, 0, 0, -21296, -1171280]$	$y^2=x^3-21296x-1171280$	58.2.0.a.1	$[ ]$
56144.i1	56144l1	56144.i	56144l	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{12} \cdot 11^{2} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$58$	$2$	$0$	$1.974561469$	$1$		$2$	$9600$	$0.158369$	$1216512/29$	$0.71531$	$2.48042$	$[0, 0, 0, -176, 880]$	$y^2=x^3-176x+880$	58.2.0.a.1	$[(9, 5)]$
56144.j1	56144c1	56144.j	56144c	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{8} \cdot 11^{8} \cdot 29^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$58$	$2$	$0$	$1$	$4$	$2$	$0$	$633600$	$2.153416$	$35780355072/20511149$	$1.20798$	$4.48340$	$[0, 0, 0, -260876, -4977940]$	$y^2=x^3-260876x-4977940$	58.2.0.a.1	$[ ]$
56144.k1	56144h2	56144.k	56144h	$2$	$2$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{13} \cdot 11^{3} \cdot 29^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2552$	$12$	$0$	$1$	$1$		$1$	$38016$	$0.714260$	$112678587/1682$	$1.00269$	$3.11380$	$[0, 0, 0, -1771, 28314]$	$y^2=x^3-1771x+28314$	2.3.0.a.1, 88.6.0.?, 232.6.0.?, 1276.6.0.?, 2552.12.0.?	$[ ]$
56144.k2	56144h1	56144.k	56144h	$2$	$2$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{14} \cdot 11^{3} \cdot 29 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2552$	$12$	$0$	$1$	$1$		$1$	$19008$	$0.367687$	$-27/116$	$0.97231$	$2.53481$	$[0, 0, 0, -11, 1210]$	$y^2=x^3-11x+1210$	2.3.0.a.1, 88.6.0.?, 232.6.0.?, 638.6.0.?, 2552.12.0.?	$[ ]$
56144.l1	56144f1	56144.l	56144f	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{8} \cdot 11^{9} \cdot 29^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1.002962279$	$1$		$2$	$253440$	$1.517448$	$-1118952448/1119371$	$0.84065$	$3.81979$	$[0, 1, 0, -16617, 1356419]$	$y^2=x^3+x^2-16617x+1356419$	22.2.0.a.1	$[(-26, 1331)]$
56144.m1	56144a1	56144.m	56144a	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{8} \cdot 11^{3} \cdot 29^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$7.230136500$	$1$		$0$	$103680$	$1.203627$	$-91029177187328/841$	$0.97322$	$4.10410$	$[0, 1, 0, -65457, -6467749]$	$y^2=x^3+x^2-65457x-6467749$	22.2.0.a.1	$[(5065/4, 137779/4)]$
56144.n1	56144k1	56144.n	56144k	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{8} \cdot 11^{9} \cdot 29^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$2.989330113$	$1$		$2$	$190080$	$1.512865$	$-524288/841$	$0.89687$	$3.80622$	$[0, 1, 0, -14197, -1269281]$	$y^2=x^3+x^2-14197x-1269281$	22.2.0.a.1	$[(1371, 50578)]$
56144.o1	56144i1	56144.o	56144i	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{8} \cdot 11^{3} \cdot 29^{2} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$0.812225354$	$1$		$8$	$17280$	$0.313917$	$-524288/841$	$0.89687$	$2.49058$	$[0, 1, 0, -117, 911]$	$y^2=x^3+x^2-117x+911$	22.2.0.a.1	$[(7, 22), (10, 29)]$
56144.p1	56144b1	56144.p	56144b	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{8} \cdot 11^{9} \cdot 29^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1$	$1$		$0$	$1140480$	$2.402573$	$-91029177187328/841$	$0.97322$	$5.41973$	$[0, 1, 0, -7920337, 8576892619]$	$y^2=x^3+x^2-7920337x+8576892619$	22.2.0.a.1	$[ ]$
56144.q1	56144e1	56144.q	56144e	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{10} \cdot 11^{6} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$116$	$2$	$0$	$4.966471847$	$1$		$2$	$43200$	$0.746494$	$48668/29$	$0.83955$	$2.93641$	$[0, 1, 0, 928, -1564]$	$y^2=x^3+x^2+928x-1564$	116.2.0.?	$[(272, 4522)]$
56144.r1	56144q2	56144.r	56144q	$2$	$5$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{14} \cdot 11^{6} \cdot 29^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$6380$	$48$	$1$	$1$	$1$		$0$	$648000$	$2.239258$	$-10418796526321/82044596$	$0.99481$	$4.81848$	$[0, 1, 0, -880920, -320690284]$	$y^2=x^3+x^2-880920x-320690284$	5.12.0.a.2, 116.2.0.?, 220.24.0.?, 580.24.1.?, 3190.24.0.?, $\ldots$	$[ ]$
56144.r2	56144q1	56144.r	56144q	$2$	$5$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{22} \cdot 11^{6} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$6380$	$48$	$1$	$1$	$1$		$0$	$129600$	$1.434540$	$13651919/29696$	$1.08166$	$3.67141$	$[0, 1, 0, 9640, 608276]$	$y^2=x^3+x^2+9640x+608276$	5.12.0.a.1, 116.2.0.?, 220.24.0.?, 580.24.1.?, 3190.24.0.?, $\ldots$	$[ ]$
56144.s1	56144m1	56144.s	56144m	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{8} \cdot 11^{8} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$58$	$2$	$0$	$1.243894782$	$1$		$2$	$88704$	$1.044832$	$90112/29$	$0.79092$	$3.30452$	$[0, -1, 0, -3549, 55409]$	$y^2=x^3-x^2-3549x+55409$	58.2.0.a.1	$[(-40, 363)]$
56144.t1	56144s1	56144.t	56144s	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ 2^{8} \cdot 11^{2} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$58$	$2$	$0$	$1$	$1$		$0$	$8064$	$-0.154116$	$90112/29$	$0.79092$	$1.98888$	$[0, -1, 0, -29, -31]$	$y^2=x^3-x^2-29x-31$	58.2.0.a.1	$[ ]$
56144.u1	56144w1	56144.u	56144w	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{14} \cdot 11^{6} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$116$	$2$	$0$	$1$	$1$		$0$	$137280$	$0.989866$	$-185193/116$	$0.85122$	$3.25246$	$[0, 0, 0, -2299, 61226]$	$y^2=x^3-2299x+61226$	116.2.0.?	$[ ]$
56144.v1	56144o1	56144.v	56144o	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{12} \cdot 11^{7} \cdot 29^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$22.65860769$	$1$		$0$	$441600$	$1.549335$	$-5601816576/9251$	$0.88114$	$4.12909$	$[0, 0, 0, -71632, -7389712]$	$y^2=x^3-71632x-7389712$	22.2.0.a.1	$[(37090454833/1164, 7142864358982103/1164)]$
56144.w1	56144v1	56144.w	56144v	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 29 $	$ - 2^{8} \cdot 11^{6} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$116$	$2$	$0$	$1$	$121$	$11$	$0$	$686400$	$1.699745$	$-48707390098512/29$	$1.02954$	$4.70473$	$[0, 0, 0, -584551, -172021102]$	$y^2=x^3-584551x-172021102$	116.2.0.?	$[ ]$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (28 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 (28 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