LMFDB - Elliptic curves over $\Q$ of conductor 726

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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

Galois image	Adelic level	Adelic index	Adelic genus

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

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Results (20 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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
726.a1	726b1	726.a	726b	$1$	$1$	$ 2 \cdot 3 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{4} \cdot 11^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.8.0.2		$44$	$16$	$0$	$1$	$1$	$0$	$5280$	$1.626667$	$43307231/82944$	$1.06329$	$6.43636$	$[1, 1, 0, 21657, -1855179]$	$y^2+xy=x^3+x^2+21657x-1855179$	4.8.0.b.1, 44.16.0-4.b.1.1	$[]$
726.b1	726a2	726.b	726a	$2$	$2$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{3} \cdot 3^{6} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.6.0.1	2B, 3Ns	$264$	$144$	$5$	$1.457269770$	$1$	$4$	$288$	$0.261843$	$8934171875/5832$	$1.11908$	$4.57026$	$[1, 1, 0, -475, -4187]$	$y^2+xy=x^3+x^2-475x-4187$	2.3.0.a.1, 3.6.0.b.1, 6.18.0.b.1, 12.36.0.b.1, 24.72.1.cd.1, $\ldots$	$[(-13, 8)]$
726.b2	726a1	726.b	726a	$2$	$2$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{6} \cdot 3^{3} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.6.0.1	2B, 3Ns	$264$	$144$	$5$	$0.728634885$	$1$	$7$	$144$	$-0.084730$	$3723875/1728$	$1.02301$	$3.38881$	$[1, 1, 0, -35, -51]$	$y^2+xy=x^3+x^2-35x-51$	2.3.0.a.1, 3.6.0.b.1, 6.36.0.b.1, 24.72.1.ce.1, 33.12.0.a.1, $\ldots$	$[(-5, 8)]$
726.c1	726c3	726.c	726c	$4$	$4$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2 \cdot 3 \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.11	2B	$264$	$48$	$0$	$1$	$1$	$0$	$1920$	$1.103994$	$4824238966273/66$	$1.02376$	$6.61734$	$[1, 1, 0, -42594, 3365850]$	$y^2+xy=x^3+x^2-42594x+3365850$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.1, 24.24.0-8.m.1.3, $\ldots$	$[]$
726.c2	726c2	726.c	726c	$4$	$4$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{2} \cdot 3^{2} \cdot 11^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$264$	$48$	$0$	$1$	$1$	$2$	$960$	$0.757421$	$1180932193/4356$	$0.96736$	$5.35509$	$[1, 1, 0, -2664, 51660]$	$y^2+xy=x^3+x^2-2664x+51660$	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.3, 44.12.0-2.a.1.1, $\ldots$	$[]$
726.c3	726c4	726.c	726c	$4$	$4$	$ 2 \cdot 3 \cdot 11^{2} $	$ - 2 \cdot 3^{4} \cdot 11^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$264$	$48$	$0$	$1$	$1$	$0$	$1920$	$1.103994$	$-192100033/2371842$	$1.02507$	$5.55094$	$[1, 1, 0, -1454, 100302]$	$y^2+xy=x^3+x^2-1454x+100302$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 24.24.0-8.d.1.3, 44.12.0-4.c.1.1, $\ldots$	$[]$
726.c4	726c1	726.c	726c	$4$	$4$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{4} \cdot 3 \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.11	2B	$264$	$48$	$0$	$1$	$1$	$1$	$480$	$0.410847$	$912673/528$	$1.18336$	$4.26737$	$[1, 1, 0, -244, -128]$	$y^2+xy=x^3+x^2-244x-128$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.1, $\ldots$	$[]$
726.d1	726e3	726.d	726e	$4$	$10$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{2} \cdot 3 \cdot 11^{11} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	8.6.0.4, 5.12.0.2	2B, 5B.4.2	$1320$	$288$	$5$	$1.514373668$	$1$	$3$	$12000$	$1.946800$	$112763292123580561/1932612$	$1.06379$	$8.14437$	$[1, 0, 1, -1217868, 517205302]$	$y^2+xy+y=x^3-1217868x+517205302$	2.3.0.a.1, 5.12.0.a.2, 8.6.0.d.1, 10.36.0.a.1, 30.72.0-10.a.1.1, $\ldots$	$[(6283/3, 63767/3)]$
726.d2	726e4	726.d	726e	$4$	$10$	$ 2 \cdot 3 \cdot 11^{2} $	$ - 2 \cdot 3^{2} \cdot 11^{16} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	8.6.0.5, 5.12.0.2	2B, 5B.4.2	$1320$	$288$	$5$	$3.028747336$	$1$	$2$	$24000$	$2.293373$	$-112427521449300721/466873642818$	$1.06387$	$8.14500$	$[1, 0, 1, -1216658, 518284622]$	$y^2+xy+y=x^3-1216658x+518284622$	2.3.0.a.1, 5.12.0.a.2, 8.6.0.a.1, 10.36.0.a.1, 40.72.1.c.2, $\ldots$	$[(582, 2431)]$
726.d3	726e1	726.d	726e	$4$	$10$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{10} \cdot 3^{5} \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	8.6.0.4, 5.12.0.1	2B, 5B.4.1	$1320$	$288$	$5$	$0.302874733$	$1$	$11$	$2400$	$1.142082$	$10091699281/2737152$	$1.07340$	$5.68077$	$[1, 0, 1, -5448, -113258]$	$y^2+xy+y=x^3-5448x-113258$	2.3.0.a.1, 5.12.0.a.1, 8.6.0.d.1, 10.36.0.a.2, 30.72.0-10.a.2.1, $\ldots$	$[(-34, 198)]$
726.d4	726e2	726.d	726e	$4$	$10$	$ 2 \cdot 3 \cdot 11^{2} $	$ - 2^{5} \cdot 3^{10} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 5$	8.6.0.5, 5.12.0.1	2B, 5B.4.1	$1320$	$288$	$5$	$0.605749467$	$1$	$8$	$4800$	$1.488655$	$168105213359/228637728$	$1.10021$	$6.15335$	$[1, 0, 1, 13912, -732778]$	$y^2+xy+y=x^3+13912x-732778$	2.3.0.a.1, 5.12.0.a.1, 8.6.0.a.1, 10.36.0.a.2, 40.72.1.c.1, $\ldots$	$[(120, 1573)]$
726.e1	726d1	726.e	726d	$1$	$1$	$ 2 \cdot 3 \cdot 11^{2} $	$ - 2^{2} \cdot 3^{4} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.8.0.2		$44$	$16$	$0$	$0.063307201$	$1$	$10$	$96$	$-0.387873$	$-2259169/324$	$0.94639$	$2.98255$	$[1, 0, 1, -14, 20]$	$y^2+xy+y=x^3-14x+20$	4.8.0.b.1, 44.16.0-4.b.1.1	$[(3, 1)]$
726.f1	726g1	726.f	726g	$1$	$1$	$ 2 \cdot 3 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{4} \cdot 11^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.16.0.2		$4$	$16$	$0$	$0.039177980$	$1$	$14$	$480$	$0.427720$	$43307231/82944$	$1.06329$	$4.25233$	$[1, 1, 1, 179, 1475]$	$y^2+xy+y=x^3+x^2+179x+1475$	4.16.0-4.b.1.1	$[(17, 90)]$
726.g1	726f2	726.g	726f	$2$	$2$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{3} \cdot 3^{6} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.6.0.1	2B, 3Ns	$264$	$144$	$5$	$1$	$1$	$0$	$3168$	$1.460791$	$8934171875/5832$	$1.11908$	$6.75429$	$[1, 1, 1, -57538, 5285303]$	$y^2+xy+y=x^3+x^2-57538x+5285303$	2.3.0.a.1, 3.6.0.b.1, 6.18.0.b.1, 12.36.0.b.1, 24.72.1.cd.1, $\ldots$	$[]$
726.g2	726f1	726.g	726f	$2$	$2$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{6} \cdot 3^{3} \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.6.0.1	2B, 3Ns	$264$	$144$	$5$	$1$	$1$	$1$	$1584$	$1.114218$	$3723875/1728$	$1.02301$	$5.57284$	$[1, 1, 1, -4298, 46487]$	$y^2+xy+y=x^3+x^2-4298x+46487$	2.3.0.a.1, 3.6.0.b.1, 6.36.0.b.1, 24.72.1.ce.1, 33.12.0.a.1, $\ldots$	$[]$
726.h1	726i1	726.h	726i	$1$	$1$	$ 2 \cdot 3 \cdot 11^{2} $	$ - 2^{2} \cdot 3^{4} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.16.0.2		$4$	$16$	$0$	$1$	$1$	$0$	$1056$	$0.811075$	$-2259169/324$	$0.94639$	$5.16657$	$[1, 0, 0, -1636, -28588]$	$y^2+xy=x^3-1636x-28588$	4.16.0-4.b.1.1	$[]$
726.i1	726h3	726.i	726h	$4$	$6$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{6} \cdot 3 \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.4, 3.4.0.1	2B, 3B	$264$	$96$	$1$	$1$	$1$	$1$	$1440$	$1.088871$	$57736239625/255552$	$0.99775$	$5.94554$	$[1, 0, 0, -9743, 367929]$	$y^2+xy=x^3-9743x+367929$	2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.1, 8.6.0.d.1, 24.48.0-24.bx.1.2, $\ldots$	$[]$
726.i2	726h4	726.i	726h	$4$	$6$	$ 2 \cdot 3 \cdot 11^{2} $	$ - 2^{3} \cdot 3^{2} \cdot 11^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.5, 3.4.0.1	2B, 3B	$264$	$96$	$1$	$1$	$1$	$0$	$2880$	$1.435444$	$-7357983625/127552392$	$1.05287$	$6.15388$	$[1, 0, 0, -4903, 734801]$	$y^2+xy=x^3-4903x+734801$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.a.1, 12.24.0-6.a.1.11, $\ldots$	$[]$
726.i3	726h1	726.i	726h	$4$	$6$	$ 2 \cdot 3 \cdot 11^{2} $	$ 2^{2} \cdot 3^{3} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.4, 3.4.0.1	2B, 3B	$264$	$96$	$1$	$1$	$1$	$1$	$480$	$0.539564$	$18609625/1188$	$0.92581$	$4.72506$	$[1, 0, 0, -668, -6324]$	$y^2+xy=x^3-668x-6324$	2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.3, 8.6.0.d.1, 24.48.0-24.bx.1.6, $\ldots$	$[]$
726.i4	726h2	726.i	726h	$4$	$6$	$ 2 \cdot 3 \cdot 11^{2} $	$ - 2 \cdot 3^{6} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.5, 3.4.0.1	2B, 3B	$264$	$96$	$1$	$1$	$1$	$0$	$960$	$0.886138$	$9938375/176418$	$1.01160$	$5.14449$	$[1, 0, 0, 542, -26410]$	$y^2+xy=x^3+542x-26410$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.a.1, 12.24.0-6.a.1.5, $\ldots$	$[]$

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

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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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