LMFDB - Elliptic curves over $\Q$ of conductor 576

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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

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

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Results (36 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	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
576.a1	576g1	576.a	576g	$2$	$2$	$ 2^{6} \cdot 3^{2} $	$ 2^{6} \cdot 3^{9} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$96$	$-0.140000$	$1728$		$3.38275$	$[0, 0, 0, -27, 0]$	$y^2=x^3-27x$		$[]$
576.a2	576g2	576.a	576g	$2$	$2$	$ 2^{6} \cdot 3^{2} $	$ - 2^{12} \cdot 3^{9} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$192$	$0.206573$	$1728$		$4.03706$	$[0, 0, 0, 108, 0]$	$y^2=x^3+108x$		$[]$
576.b1	576i5	576.b	576i	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ 2^{17} \cdot 3^{8} $	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.96.0.269	2B	$48$	$192$	$1$	$4.317095458$	$1$	$3$	$512$	$0.943675$	$3065617154/9$	$1.21059$	$6.32757$	$[0, 0, 0, -13836, -626416]$	$y^2=x^3-13836x-626416$	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.r.1.3, 12.12.0-4.c.1.2, 16.96.0-16.l.1.4, $\ldots$	$[(157, 1035)]$
576.b2	576i4	576.b	576i	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ 2^{16} \cdot 3^{7} $	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.96.0.224	2B	$48$	$192$	$1$	$0.539636932$	$1$	$9$	$256$	$0.597101$	$28756228/3$	$1.05617$	$5.48392$	$[0, 0, 0, -2316, 42896]$	$y^2=x^3-2316x+42896$	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.2.8, 12.12.0.h.1, 16.96.0-16.bb.2.8, $\ldots$	$[(26, 16)]$
576.b3	576i3	576.b	576i	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ 2^{16} \cdot 3^{10} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.96.0.135	2Cs	$24$	$192$	$1$	$2.158547729$	$1$	$9$	$256$	$0.597101$	$1556068/81$	$1.03212$	$5.02504$	$[0, 0, 0, -876, -9520]$	$y^2=x^3-876x-9520$	2.6.0.a.1, 4.12.0.b.1, 8.96.0-8.e.2.8, 12.24.0-4.b.1.2, 24.192.1-24.bl.2.6	$[(-16, 20)]$
576.b4	576i2	576.b	576i	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ 2^{14} \cdot 3^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.96.0.113	2Cs	$24$	$192$	$1$	$1.079273864$	$1$	$11$	$128$	$0.250527$	$35152/9$	$0.97255$	$4.21062$	$[0, 0, 0, -156, 560]$	$y^2=x^3-156x+560$	2.6.0.a.1, 4.12.0.b.1, 8.96.0-8.h.1.8, 12.24.0.c.1, 24.192.1-24.bu.1.4	$[(2, 16)]$
576.b5	576i1	576.b	576i	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ - 2^{10} \cdot 3^{7} $	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.96.0.303	2B	$48$	$192$	$1$	$0.539636932$	$1$	$9$	$64$	$-0.096046$	$2048/3$	$1.17572$	$3.39419$	$[0, 0, 0, 24, 56]$	$y^2=x^3+24x+56$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.48.0-8.ba.1.3, 12.12.0.g.1, $\ldots$	$[(1, 9)]$
576.b6	576i6	576.b	576i	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ - 2^{17} \cdot 3^{14} $	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.96.0.252	2B	$48$	$192$	$1$	$1.079273864$	$1$	$7$	$512$	$0.943675$	$207646/6561$	$1.15980$	$5.44363$	$[0, 0, 0, 564, -37744]$	$y^2=x^3+564x-37744$	2.3.0.a.1, 4.6.0.c.1, 8.48.0.m.1, 12.12.0-4.c.1.1, 16.96.0-8.m.1.1, $\ldots$	$[(34, 144)]$
576.c1	576h3	576.c	576h	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ 2^{15} \cdot 3^{6} $	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$	✓							$1.777251749$	$1$	$5$	$128$	$0.278494$	$287496$	$1.17246$	$4.65031$	$[0, 0, 0, -396, -3024]$	$y^2=x^3-396x-3024$		$[(-11, 1)]$
576.c2	576h4	576.c	576h	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ 2^{15} \cdot 3^{6} $	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$	✓							$0.444312937$	$1$	$9$	$128$	$0.278494$	$287496$	$1.17246$	$4.65031$	$[0, 0, 0, -396, 3024]$	$y^2=x^3-396x+3024$		$[(10, 8)]$
576.c3	576h2	576.c	576h	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ 2^{12} \cdot 3^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$	✓	$2$	16.192.9.143	2Cs				$0.888625874$	$1$	$13$	$64$	$-0.068080$	$1728$		$3.51853$	$[0, 0, 0, -36, 0]$	$y^2=x^3-36x$		$[(-3, 9)]$
576.c4	576h1	576.c	576h	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ - 2^{6} \cdot 3^{6} $	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$	✓	$2$	16.192.9.178	2B				$1.777251749$	$1$	$3$	$32$	$-0.414653$	$1728$		$2.86422$	$[0, 0, 0, 9, 0]$	$y^2=x^3+9x$		$[(4, 10)]$
576.d1	576d5	576.d	576d	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ 2^{17} \cdot 3^{8} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.96.0.234	2B	$48$	$192$	$1$	$1$	$1$	$1$	$512$	$0.943675$	$3065617154/9$	$1.21059$	$6.32757$	$[0, 0, 0, -13836, 626416]$	$y^2=x^3-13836x+626416$	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.r.1.4, 12.12.0-4.c.1.1, 16.96.0-16.l.1.8, $\ldots$	$[]$
576.d2	576d3	576.d	576d	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ 2^{16} \cdot 3^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.96.0.284	2B	$48$	$192$	$1$	$1$	$1$	$1$	$256$	$0.597101$	$28756228/3$	$1.05617$	$5.48392$	$[0, 0, 0, -2316, -42896]$	$y^2=x^3-2316x-42896$	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.2.7, 12.12.0.h.1, 16.96.0-16.bb.2.7, $\ldots$	$[]$
576.d3	576d4	576.d	576d	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ 2^{16} \cdot 3^{10} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.96.0.103	2Cs	$24$	$192$	$1$	$1$	$1$	$3$	$256$	$0.597101$	$1556068/81$	$1.03212$	$5.02504$	$[0, 0, 0, -876, 9520]$	$y^2=x^3-876x+9520$	2.6.0.a.1, 4.12.0.b.1, 8.96.0-8.e.2.7, 12.24.0-4.b.1.2, 24.192.1-24.bl.2.8	$[]$
576.d4	576d2	576.d	576d	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ 2^{14} \cdot 3^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.96.0.147	2Cs	$24$	$192$	$1$	$1$	$1$	$3$	$128$	$0.250527$	$35152/9$	$0.97255$	$4.21062$	$[0, 0, 0, -156, -560]$	$y^2=x^3-156x-560$	2.6.0.a.1, 4.12.0.b.1, 8.96.0-8.h.1.4, 12.24.0.c.1, 24.192.1-24.bu.1.6	$[]$
576.d5	576d1	576.d	576d	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ - 2^{10} \cdot 3^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.96.0.268	2B	$48$	$192$	$1$	$1$	$1$	$1$	$64$	$-0.096046$	$2048/3$	$1.17572$	$3.39419$	$[0, 0, 0, 24, -56]$	$y^2=x^3+24x-56$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.48.0-8.ba.1.4, 12.12.0.g.1, $\ldots$	$[]$
576.d6	576d6	576.d	576d	$6$	$8$	$ 2^{6} \cdot 3^{2} $	$ - 2^{17} \cdot 3^{14} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.96.0.250	2B	$48$	$192$	$1$	$1$	$1$	$1$	$512$	$0.943675$	$207646/6561$	$1.15980$	$5.44363$	$[0, 0, 0, 564, 37744]$	$y^2=x^3+564x+37744$	2.3.0.a.1, 4.6.0.c.1, 8.48.0.m.1, 12.12.0-4.c.1.2, 16.96.0-8.m.1.3, $\ldots$	$[]$
576.e1	576a4	576.e	576a	$4$	$6$	$ 2^{6} \cdot 3^{2} $	$ 2^{14} \cdot 3^{9} $	$1$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-12$	$N(\mathrm{U}(1))$	✓							$0.979852016$	$1$	$7$	$192$	$0.427038$	$54000$	$1.02720$	$4.79670$	$[0, 0, 0, -540, -4752]$	$y^2=x^3-540x-4752$		$[(-14, 8)]$
576.e2	576a2	576.e	576a	$4$	$6$	$ 2^{6} \cdot 3^{2} $	$ 2^{14} \cdot 3^{3} $	$1$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-12$	$N(\mathrm{U}(1))$	✓							$0.326617338$	$1$	$9$	$64$	$-0.122268$	$54000$	$1.02720$	$3.75963$	$[0, 0, 0, -60, 176]$	$y^2=x^3-60x+176$		$[(2, 8)]$
576.e3	576a3	576.e	576a	$4$	$6$	$ 2^{6} \cdot 3^{2} $	$ - 2^{10} \cdot 3^{9} $	$1$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$	✓	$2$	16.192.9.83	2B				$1.959704032$	$1$	$5$	$96$	$0.080464$	$0$		$3.81896$	$[0, 0, 0, 0, -216]$	$y^2=x^3-216$		$[(10, 28)]$
576.e4	576a1	576.e	576a	$4$	$6$	$ 2^{6} \cdot 3^{2} $	$ - 2^{10} \cdot 3^{3} $	$1$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$	✓	$2$	16.192.9.83	2B				$0.653234677$	$1$	$7$	$32$	$-0.468842$	$0$		$2.78190$	$[0, 0, 0, 0, 8]$	$y^2=x^3+8$		$[(1, 3)]$
576.f1	576e4	576.f	576e	$4$	$6$	$ 2^{6} \cdot 3^{2} $	$ 2^{14} \cdot 3^{9} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-12$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$192$	$0.427038$	$54000$	$1.02720$	$4.79670$	$[0, 0, 0, -540, 4752]$	$y^2=x^3-540x+4752$		$[]$
576.f2	576e2	576.f	576e	$4$	$6$	$ 2^{6} \cdot 3^{2} $	$ 2^{14} \cdot 3^{3} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-12$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$64$	$-0.122268$	$54000$	$1.02720$	$3.75963$	$[0, 0, 0, -60, -176]$	$y^2=x^3-60x-176$		$[]$
576.f3	576e1	576.f	576e	$4$	$6$	$ 2^{6} \cdot 3^{2} $	$ - 2^{10} \cdot 3^{3} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$	✓	$2$	16.192.9.83	2B				$1$	$1$	$1$	$32$	$-0.468842$	$0$		$2.78190$	$[0, 0, 0, 0, -8]$	$y^2=x^3-8$		$[]$
576.f4	576e3	576.f	576e	$4$	$6$	$ 2^{6} \cdot 3^{2} $	$ - 2^{10} \cdot 3^{9} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$	✓	$2$	16.192.9.83	2B				$1$	$1$	$1$	$96$	$0.080464$	$0$		$3.81896$	$[0, 0, 0, 0, 216]$	$y^2=x^3+216$		$[]$
576.g1	576c3	576.g	576c	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ 2^{15} \cdot 3^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.24.0.110	2B	$24$	$48$	$0$	$1$	$1$	$1$	$256$	$0.469659$	$7301384/3$	$1.03749$	$5.15920$	$[0, 0, 0, -1164, -15280]$	$y^2=x^3-1164x-15280$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.4, 12.12.0-4.c.1.2, 24.48.0-24.bi.1.6	$[]$
576.g2	576c2	576.g	576c	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ 2^{12} \cdot 3^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.24.0.8	2Cs	$24$	$48$	$0$	$1$	$1$	$3$	$128$	$0.123086$	$21952/9$	$1.09175$	$3.91844$	$[0, 0, 0, -84, -160]$	$y^2=x^3-84x-160$	2.6.0.a.1, 4.12.0-2.a.1.2, 8.24.0-8.b.1.4, 12.24.0-12.a.1.4, 24.48.0-24.f.1.6	$[]$
576.g3	576c1	576.g	576c	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ 2^{6} \cdot 3^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.24.0.114	2B	$24$	$48$	$0$	$1$	$1$	$1$	$64$	$-0.223488$	$140608/3$	$1.02705$	$3.55631$	$[0, 0, 0, -39, 92]$	$y^2=x^3-39x+92$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.2, 12.12.0.h.1, 24.48.0-24.bk.1.7	$[]$
576.g4	576c4	576.g	576c	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ - 2^{15} \cdot 3^{10} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.24.0.118	2B	$24$	$48$	$0$	$1$	$1$	$1$	$256$	$0.469659$	$97336/81$	$1.05989$	$4.47991$	$[0, 0, 0, 276, -1168]$	$y^2=x^3+276x-1168$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.d.1.4, 12.12.0-4.c.1.1, 24.48.0-24.n.1.1	$[]$
576.h1	576b3	576.h	576b	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ 2^{15} \cdot 3^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.24.0.114	2B	$24$	$48$	$0$	$1$	$1$	$1$	$256$	$0.469659$	$7301384/3$	$1.03749$	$5.15920$	$[0, 0, 0, -1164, 15280]$	$y^2=x^3-1164x+15280$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.2, 12.12.0-4.c.1.1, 24.48.0-24.bi.1.5	$[]$
576.h2	576b2	576.h	576b	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ 2^{12} \cdot 3^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.24.0.8	2Cs	$24$	$48$	$0$	$1$	$1$	$3$	$128$	$0.123086$	$21952/9$	$1.09175$	$3.91844$	$[0, 0, 0, -84, 160]$	$y^2=x^3-84x+160$	2.6.0.a.1, 4.12.0-2.a.1.2, 8.24.0-8.b.1.4, 12.24.0-12.a.1.4, 24.48.0-24.f.1.7	$[]$
576.h3	576b1	576.h	576b	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ 2^{6} \cdot 3^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.24.0.110	2B	$24$	$48$	$0$	$1$	$1$	$1$	$64$	$-0.223488$	$140608/3$	$1.02705$	$3.55631$	$[0, 0, 0, -39, -92]$	$y^2=x^3-39x-92$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.4, 12.12.0.h.1, 24.48.0-24.bk.1.6	$[]$
576.h4	576b4	576.h	576b	$4$	$4$	$ 2^{6} \cdot 3^{2} $	$ - 2^{15} \cdot 3^{10} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	8.24.0.118	2B	$24$	$48$	$0$	$1$	$1$	$1$	$256$	$0.469659$	$97336/81$	$1.05989$	$4.47991$	$[0, 0, 0, 276, 1168]$	$y^2=x^3+276x+1168$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.d.1.4, 12.12.0-4.c.1.2, 24.48.0-24.n.1.3	$[]$
576.i1	576f1	576.i	576f	$2$	$2$	$ 2^{6} \cdot 3^{2} $	$ 2^{6} \cdot 3^{3} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$32$	$-0.689306$	$1728$		$2.34569$	$[0, 0, 0, -3, 0]$	$y^2=x^3-3x$		$[]$
576.i2	576f2	576.i	576f	$2$	$2$	$ 2^{6} \cdot 3^{2} $	$ - 2^{12} \cdot 3^{3} $	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$	✓							$1$	$1$	$1$	$64$	$-0.342733$	$1728$		$3.00000$	$[0, 0, 0, 12, 0]$	$y^2=x^3+12x$		$[]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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Results (36 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