LMFDB - Elliptic curves over $\Q$ of conductor 27735

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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 (26 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
27735.a1	27735k1	27735.a	27735k	$1$	$1$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{14} \cdot 5^{2} \cdot 43^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$86$	$2$	$0$	$0.993905046$	$1$		$4$	$4967424$	$3.166874$	$-522547125460258816/9506987907075$	$1.00952$	$6.19676$	$[0, 1, 1, -31026836, -67568222734]$	$y^2+y=x^3+x^2-31026836x-67568222734$	86.2.0.?	$[(8872, 596302)]$
27735.b1	27735e2	27735.b	27735e	$2$	$2$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{5} \cdot 5^{10} \cdot 43^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$9$	$3$	$0$	$7189600$	$3.432713$	$206246988924787/2373046875$	$1.00677$	$6.53059$	$[1, 1, 1, -97864835, -368956593088]$	$y^2+xy+y=x^3+x^2-97864835x-368956593088$	2.3.0.a.1, 60.6.0.d.1, 258.6.0.?, 860.6.0.?, 2580.12.0.?	$[]$
27735.b2	27735e1	27735.b	27735e	$2$	$2$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{10} \cdot 5^{5} \cdot 43^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$9$	$3$	$1$	$3594800$	$3.086140$	$-444194947/184528125$	$1.05268$	$5.89810$	$[1, 1, 1, -1263830, -14662747150]$	$y^2+xy+y=x^3+x^2-1263830x-14662747150$	2.3.0.a.1, 60.6.0.d.1, 430.6.0.?, 516.6.0.?, 2580.12.0.?	$[]$
27735.c1	27735i1	27735.c	27735i	$2$	$2$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{3} \cdot 5^{2} \cdot 43^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.290931459$	$1$		$3$	$133056$	$1.523252$	$1263214441/29025$	$0.85169$	$4.25437$	$[1, 0, 0, -41641, -3208504]$	$y^2+xy=x^3-41641x-3208504$	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(283, 2632)]$
27735.c2	27735i2	27735.c	27735i	$2$	$2$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{6} \cdot 5 \cdot 43^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.581862919$	$1$		$2$	$266112$	$1.869825$	$1685159/6739605$	$1.19354$	$4.47148$	$[1, 0, 0, 4584, -9929619]$	$y^2+xy=x^3+4584x-9929619$	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(2820, 148359)]$
27735.d1	27735h1	27735.d	27735h	$1$	$1$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{15} \cdot 5 \cdot 43^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$60$	$2$	$0$	$0.240988587$	$1$		$6$	$30240$	$0.861986$	$539033907481/71744535$	$0.95490$	$3.37575$	$[1, 0, 0, -2081, 31890]$	$y^2+xy=x^3-2081x+31890$	60.2.0.a.1	$[(61, 334)]$
27735.e1	27735m1	27735.e	27735m	$1$	$1$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{5} \cdot 5^{5} \cdot 43^{2} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$60$	$2$	$0$	$0.164633928$	$1$		$22$	$16800$	$0.489242$	$7037694889/759375$	$0.91796$	$2.95167$	$[1, 0, 0, -490, 3725]$	$y^2+xy=x^3-490x+3725$	60.2.0.a.1	$[(5, 35), (35, 155)]$
27735.f1	27735l4	27735.f	27735l	$4$	$4$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3 \cdot 5^{4} \cdot 43^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$5160$	$48$	$0$	$1$	$9$	$3$	$0$	$325248$	$2.067245$	$36097320816649/80625$	$0.94094$	$5.25729$	$[1, 0, 0, -1273075, -552982768]$	$y^2+xy=x^3-1273075x-552982768$	2.3.0.a.1, 4.12.0-4.c.1.2, 120.24.0.?, 258.6.0.?, 516.24.0.?, $\ldots$	$[]$
27735.f2	27735l3	27735.f	27735l	$4$	$4$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3 \cdot 5 \cdot 43^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$5160$	$48$	$0$	$1$	$9$	$3$	$0$	$325248$	$2.067245$	$184122897769/51282015$	$1.05622$	$4.74134$	$[1, 0, 0, -219145, 28420490]$	$y^2+xy=x^3-219145x+28420490$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 60.12.0.h.1, 120.24.0.?, $\ldots$	$[]$
27735.f3	27735l2	27735.f	27735l	$4$	$4$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{2} \cdot 5^{2} \cdot 43^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2580$	$48$	$0$	$1$	$9$	$3$	$2$	$162624$	$1.720671$	$9116230969/416025$	$0.87424$	$4.44756$	$[1, 0, 0, -80470, -8439325]$	$y^2+xy=x^3-80470x-8439325$	2.6.0.a.1, 4.12.0-2.a.1.1, 60.24.0-60.a.1.6, 516.24.0.?, 860.24.0.?, $\ldots$	$[]$
27735.f4	27735l1	27735.f	27735l	$4$	$4$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{4} \cdot 5 \cdot 43^{7} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$5160$	$48$	$0$	$1$	$9$	$3$	$3$	$81312$	$1.374098$	$357911/17415$	$0.85974$	$3.88791$	$[1, 0, 0, 2735, -501568]$	$y^2+xy=x^3+2735x-501568$	2.3.0.a.1, 4.12.0-4.c.1.1, 120.24.0.?, 430.6.0.?, 860.24.0.?, $\ldots$	$[]$
27735.g1	27735b1	27735.g	27735b	$1$	$1$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{12} \cdot 5^{8} \cdot 43^{7} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$86$	$2$	$0$	$6.602719998$	$1$		$2$	$2838528$	$3.046360$	$660867352100864/8926548046875$	$1.07121$	$5.84512$	$[0, -1, 1, 3355319, -11182531644]$	$y^2+y=x^3-x^2+3355319x-11182531644$	86.2.0.?	$[(16042/3, 577799/3), (13588, 1594687)]$
27735.h1	27735a1	27735.h	27735a	$1$	$1$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{5} \cdot 5^{5} \cdot 43^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$60$	$2$	$0$	$10.29875012$	$1$		$0$	$722400$	$2.369843$	$7037694889/759375$	$0.91796$	$5.15756$	$[1, 1, 0, -906048, -299787723]$	$y^2+xy=x^3+x^2-906048x-299787723$	60.2.0.a.1	$[(4429708/9, 9301901509/9)]$
27735.i1	27735d1	27735.i	27735d	$1$	$1$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{15} \cdot 5 \cdot 43^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$60$	$2$	$0$	$1$	$16$	$2$	$0$	$1300320$	$2.742584$	$539033907481/71744535$	$0.95490$	$5.58164$	$[1, 1, 0, -3847807, -2550869414]$	$y^2+xy=x^3+x^2-3847807x-2550869414$	60.2.0.a.1	$[]$
27735.j1	27735f2	27735.j	27735f	$2$	$2$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{5} \cdot 5^{10} \cdot 43^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$167200$	$1.552114$	$206246988924787/2373046875$	$1.00677$	$4.32471$	$[1, 0, 1, -52929, 4635631]$	$y^2+xy+y=x^3-52929x+4635631$	2.3.0.a.1, 60.6.0.d.1, 258.6.0.?, 860.6.0.?, 2580.12.0.?	$[]$
27735.j2	27735f1	27735.j	27735f	$2$	$2$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{10} \cdot 5^{5} \cdot 43^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$83600$	$1.205540$	$-444194947/184528125$	$1.05268$	$3.69222$	$[1, 0, 1, -684, 184357]$	$y^2+xy+y=x^3-684x+184357$	2.3.0.a.1, 60.6.0.d.1, 430.6.0.?, 516.6.0.?, 2580.12.0.?	$[]$
27735.k1	27735g8	27735.k	27735g	$8$	$16$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{4} \cdot 5 \cdot 43^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.121	2B	$20640$	$768$	$13$	$6.481644899$	$1$		$0$	$322560$	$2.171471$	$1114544804970241/405$	$1.07354$	$5.59256$	$[1, 0, 1, -3993879, 3071802841]$	$y^2+xy+y=x^3-3993879x+3071802841$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$	$[(5399/2, 89433/2)]$
27735.k2	27735g6	27735.k	27735g	$8$	$16$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{8} \cdot 5^{2} \cdot 43^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.123	2Cs	$10320$	$768$	$13$	$3.240822449$	$1$		$4$	$161280$	$1.824896$	$272223782641/164025$	$1.03897$	$4.77956$	$[1, 0, 1, -249654, 47966731]$	$y^2+xy+y=x^3-249654x+47966731$	2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$	$[(-37, 7578)]$
27735.k3	27735g7	27735.k	27735g	$8$	$16$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{16} \cdot 5 \cdot 43^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.134	2B	$20640$	$768$	$13$	$1.620411224$	$1$		$0$	$322560$	$2.171471$	$-147281603041/215233605$	$1.05949$	$4.84268$	$[1, 0, 1, -203429, 66290321]$	$y^2+xy+y=x^3-203429x+66290321$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$	$[(2379/2, 97463/2)]$
27735.k4	27735g4	27735.k	27735g	$8$	$16$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3 \cdot 5 \cdot 43^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.1	2B	$20640$	$768$	$13$	$25.92657959$	$1$		$0$	$80640$	$1.478323$	$56667352321/15$	$1.03019$	$4.62616$	$[1, 0, 1, -147959, -21918073]$	$y^2+xy+y=x^3-147959x-21918073$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$	$[(6943956090785/62816, 17601200266788884673/62816)]$
27735.k5	27735g3	27735.k	27735g	$8$	$16$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{4} \cdot 5^{4} \cdot 43^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.44	2Cs	$10320$	$768$	$13$	$6.481644899$	$1$		$2$	$80640$	$1.478323$	$111284641/50625$	$1.02534$	$4.01691$	$[1, 0, 1, -18529, 447431]$	$y^2+xy+y=x^3-18529x+447431$	2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$	$[(-803/7, 299039/7)]$
27735.k6	27735g2	27735.k	27735g	$8$	$16$	$ 3 \cdot 5 \cdot 43^{2} $	$ 3^{2} \cdot 5^{2} \cdot 43^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.3	2Cs	$10320$	$768$	$13$	$12.96328979$	$1$		$2$	$40320$	$1.131748$	$13997521/225$	$0.96230$	$3.81426$	$[1, 0, 1, -9284, -340243]$	$y^2+xy+y=x^3-9284x-340243$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$	$[(-905973/133, -33080186/133)]$
27735.k7	27735g1	27735.k	27735g	$8$	$16$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3 \cdot 5 \cdot 43^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.1	2B	$20640$	$768$	$13$	$25.92657959$	$1$		$1$	$20160$	$0.785175$	$-1/15$	$1.19808$	$3.19927$	$[1, 0, 1, -39, -14819]$	$y^2+xy+y=x^3-39x-14819$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$	$[(175608467329/20083, 71829520009567697/20083)]$
27735.k8	27735g5	27735.k	27735g	$8$	$16$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{2} \cdot 5^{8} \cdot 43^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.197	2B	$20640$	$768$	$13$	$12.96328979$	$1$		$0$	$161280$	$1.824896$	$4733169839/3515625$	$1.05585$	$4.38349$	$[1, 0, 1, 64676, 3376247]$	$y^2+xy+y=x^3+64676x+3376247$	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$	$[(12775519/182, 54653658487/182)]$
27735.l1	27735c1	27735.l	27735c	$1$	$1$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{6} \cdot 5^{2} \cdot 43^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$86$	$2$	$0$	$1$	$1$		$0$	$354816$	$1.693045$	$99897344/783675$	$0.89128$	$4.25368$	$[0, -1, 1, 17874, -3265009]$	$y^2+y=x^3-x^2+17874x-3265009$	86.2.0.?	$[]$
27735.m1	27735j1	27735.m	27735j	$1$	$1$	$ 3 \cdot 5 \cdot 43^{2} $	$ - 3^{6} \cdot 5^{2} \cdot 43^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$86$	$2$	$0$	$0.838589495$	$1$		$0$	$2128896$	$2.723064$	$-645008376471556096/783675$	$1.01002$	$6.21431$	$[0, 1, 1, -33282616, 73893987601]$	$y^2+y=x^3+x^2-33282616x+73893987601$	86.2.0.?	$[(12053/2, 249611/2)]$

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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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