LMFDB - Elliptic curves over $\Q$ of conductor 585

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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 (21 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
585.a1	585g1	585.a	585g	$1$	$1$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{7} \cdot 5 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.099517256$	$1$	$10$	$96$	$-0.331278$	$-4096/195$	$0.83662$	$3.03400$	$[0, 0, 1, -3, 18]$	$y^2+y=x^3-3x+18$	390.2.0.?	$[(-1, 4)]$
585.b1	585e1	585.b	585e	$1$	$1$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{13} \cdot 5 \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$1$	$1$	$0$	$672$	$0.741874$	$-762549907456/24024195$	$0.97132$	$5.33689$	$[0, 0, 1, -1713, -28022]$	$y^2+y=x^3-1713x-28022$	390.2.0.?	$[]$
585.c1	585i1	585.c	585i	$1$	$1$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{9} \cdot 5^{7} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.037671158$	$1$	$16$	$672$	$0.674158$	$-32278933504/27421875$	$0.96372$	$4.97406$	$[0, 0, 1, -597, 8820]$	$y^2+y=x^3-597x+8820$	390.2.0.?	$[(8, 67)]$
585.d1	585a2	585.d	585a	$2$	$2$	$ 3^{2} \cdot 5 \cdot 13 $	$ 3^{9} \cdot 5^{2} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.395894122$	$1$	$8$	$384$	$0.652084$	$260549802603/4225$	$0.95689$	$5.67730$	$[1, -1, 1, -3593, 83782]$	$y^2+xy+y=x^3-x^2-3593x+83782$	2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.?	$[(28, 53)]$
585.d2	585a1	585.d	585a	$2$	$2$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{9} \cdot 5^{4} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.791788244$	$1$	$7$	$192$	$0.305511$	$-57960603/8125$	$0.86399$	$4.39131$	$[1, -1, 1, -218, 1432]$	$y^2+xy+y=x^3-x^2-218x+1432$	2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.?	$[(8, 8)]$
585.e1	585b2	585.e	585b	$2$	$3$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{9} \cdot 5^{3} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$390$	$16$	$0$	$1$	$1$	$0$	$144$	$0.284592$	$-303464448/1625$	$0.94004$	$4.61853$	$[0, 0, 1, -378, -2842]$	$y^2+y=x^3-378x-2842$	3.8.0-3.a.1.1, 390.16.0.?	$[]$
585.e2	585b1	585.e	585b	$2$	$3$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{3} \cdot 5 \cdot 13^{3} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$390$	$16$	$0$	$1$	$1$	$2$	$48$	$-0.264715$	$7077888/10985$	$1.00193$	$3.07430$	$[0, 0, 1, 12, -21]$	$y^2+y=x^3+12x-21$	3.8.0-3.a.1.2, 390.16.0.?	$[]$
585.f1	585d1	585.f	585d	$2$	$3$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{3} \cdot 5^{3} \cdot 13 $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$390$	$16$	$0$	$0.766940191$	$1$	$8$	$48$	$-0.264715$	$-303464448/1625$	$0.94004$	$3.58399$	$[0, 0, 1, -42, 105]$	$y^2+y=x^3-42x+105$	3.8.0-3.a.1.2, 390.16.0.?	$[(5, 4)]$
585.f2	585d2	585.f	585d	$2$	$3$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{9} \cdot 5 \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$390$	$16$	$0$	$0.255646730$	$1$	$4$	$144$	$0.284592$	$7077888/10985$	$1.00193$	$4.10884$	$[0, 0, 1, 108, 560]$	$y^2+y=x^3+108x+560$	3.8.0-3.a.1.1, 390.16.0.?	$[(30, 175)]$
585.g1	585f7	585.g	585f	$8$	$16$	$ 3^{2} \cdot 5 \cdot 13 $	$ 3^{7} \cdot 5^{4} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.171	2B	$6240$	$768$	$13$	$1.386213803$	$1$	$2$	$3072$	$1.738724$	$242970740812818720001/24375$	$1.04119$	$8.40151$	$[1, -1, 0, -1170000, 487402461]$	$y^2+xy=x^3-x^2-1170000x+487402461$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.3, 12.12.0-4.c.1.1, 16.48.0-16.g.1.4, $\ldots$	$[(588, 1281)]$
585.g2	585f5	585.g	585f	$8$	$16$	$ 3^{2} \cdot 5 \cdot 13 $	$ 3^{8} \cdot 5^{8} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.108	2Cs	$3120$	$768$	$13$	$2.772427606$	$1$	$4$	$1536$	$1.392149$	$59319456301170001/594140625$	$1.01234$	$7.09607$	$[1, -1, 0, -73125, 7629336]$	$y^2+xy=x^3-x^2-73125x+7629336$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.i.1.8, 12.24.0-4.b.1.1, 24.96.0-24.bb.1.4, $\ldots$	$[(120, 696)]$
585.g3	585f8	585.g	585f	$8$	$16$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{7} \cdot 5^{16} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.110	2B	$6240$	$768$	$13$	$5.544855213$	$1$	$0$	$3072$	$1.738724$	$-55150149867714721/5950927734375$	$1.01425$	$7.11146$	$[1, -1, 0, -71370, 8011575]$	$y^2+xy=x^3-x^2-71370x+8011575$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 12.12.0-4.c.1.1, 16.48.0-16.g.1.8, $\ldots$	$[(519/2, 7167/2)]$
585.g4	585f3	585.g	585f	$8$	$16$	$ 3^{2} \cdot 5 \cdot 13 $	$ 3^{10} \cdot 5^{4} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.42	2Cs	$3120$	$768$	$13$	$1.386213803$	$1$	$6$	$768$	$1.045576$	$15551989015681/1445900625$	$0.97384$	$5.80181$	$[1, -1, 0, -4680, 114075]$	$y^2+xy=x^3-x^2-4680x+114075$	2.6.0.a.1, 4.24.0.b.1, 8.48.0-4.b.1.4, 12.48.0-4.b.1.1, 24.96.0-24.b.1.12, $\ldots$	$[(78, 429)]$
585.g5	585f2	585.g	585f	$8$	$16$	$ 3^{2} \cdot 5 \cdot 13 $	$ 3^{14} \cdot 5^{2} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.4	2Cs	$3120$	$768$	$13$	$2.772427606$	$1$	$6$	$384$	$0.699002$	$168288035761/27720225$	$1.01793$	$5.09143$	$[1, -1, 0, -1035, -10584]$	$y^2+xy=x^3-x^2-1035x-10584$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 12.24.0-4.b.1.3, 16.48.0-8.i.1.3, $\ldots$	$[(40, 84)]$
585.g6	585f1	585.g	585f	$8$	$16$	$ 3^{2} \cdot 5 \cdot 13 $	$ 3^{10} \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.3	2B	$6240$	$768$	$13$	$5.544855213$	$1$	$3$	$192$	$0.352429$	$147281603041/5265$	$0.93867$	$5.07050$	$[1, -1, 0, -990, -11745]$	$y^2+xy=x^3-x^2-990x-11745$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0.g.1, $\ldots$	$[(238, 3513)]$
585.g7	585f4	585.g	585f	$8$	$16$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{22} \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.3	2B	$6240$	$768$	$13$	$5.544855213$	$1$	$0$	$768$	$1.045576$	$1023887723039/2798036865$	$1.05353$	$5.58110$	$[1, -1, 0, 1890, -61479]$	$y^2+xy=x^3-x^2+1890x-61479$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0.g.1, $\ldots$	$[(115/2, 897/2)]$
585.g8	585f6	585.g	585f	$8$	$16$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{8} \cdot 5^{2} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.196	2B	$6240$	$768$	$13$	$0.693106901$	$1$	$4$	$1536$	$1.392149$	$24487529386319/183539412225$	$1.01498$	$6.26242$	$[1, -1, 0, 5445, 533250]$	$y^2+xy=x^3-x^2+5445x+533250$	2.3.0.a.1, 4.12.0.d.1, 8.48.0-8.q.1.4, 12.24.0-4.d.1.1, 24.96.0-24.be.2.11, $\ldots$	$[(-30, 600)]$
585.h1	585h1	585.h	585h	$2$	$2$	$ 3^{2} \cdot 5 \cdot 13 $	$ 3^{6} \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1560$	$48$	$0$	$1.638175766$	$1$	$3$	$48$	$-0.412309$	$117649/65$	$0.95681$	$2.86696$	$[1, -1, 0, -9, 0]$	$y^2+xy=x^3-x^2-9x$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 130.6.0.?, 260.24.0.?, $\ldots$	$[(4, 2)]$
585.h2	585h2	585.h	585h	$2$	$2$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{6} \cdot 5^{2} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$1560$	$48$	$0$	$0.819087883$	$1$	$4$	$96$	$-0.065735$	$6967871/4225$	$0.89914$	$3.50751$	$[1, -1, 0, 36, -27]$	$y^2+xy=x^3-x^2+36x-27$	2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.1, 260.12.0.?, 520.24.0.?, $\ldots$	$[(4, 11)]$
585.i1	585c2	585.i	585c	$2$	$2$	$ 3^{2} \cdot 5 \cdot 13 $	$ 3^{3} \cdot 5^{2} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$	$0$	$128$	$0.102778$	$260549802603/4225$	$0.95689$	$4.64277$	$[1, -1, 0, -399, -2970]$	$y^2+xy=x^3-x^2-399x-2970$	2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.?	$[]$
585.i2	585c1	585.i	585c	$2$	$2$	$ 3^{2} \cdot 5 \cdot 13 $	$ - 3^{3} \cdot 5^{4} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$	$1$	$64$	$-0.243795$	$-57960603/8125$	$0.86399$	$3.35677$	$[1, -1, 0, -24, -45]$	$y^2+xy=x^3-x^2-24x-45$	2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.?	$[]$

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Elliptic 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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