LMFDB - Elliptic curves over $\Q$ of conductor 6042

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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 (23 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	Semistable	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
6042.a1	6042d1	6042.a	6042d	$1$	$1$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ - 2^{5} \cdot 3^{6} \cdot 19^{3} \cdot 53 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$8056$	$2$	$0$	$0.278381172$	$1$		$4$	$7920$	$0.769787$	$-2537325859890457/8480357856$	$1.01218$	$4.07462$	$[1, 1, 0, -2841, 57285]$	$y^2+xy=x^3+x^2-2841x+57285$	8056.2.0.?	$[(-3, 258)]$
6042.b1	6042a1	6042.b	6042a	$1$	$1$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{10} \cdot 3^{3} \cdot 19^{3} \cdot 53 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$6042$	$2$	$0$	$0.526311139$	$1$		$14$	$4320$	$0.620138$	$28119423707929/10050794496$	$0.90995$	$3.55683$	$[1, 1, 0, -633, -4059]$	$y^2+xy=x^3+x^2-633x-4059$	6042.2.0.?	$[(50, 279), (-7, -6)]$
6042.c1	6042c4	6042.c	6042c	$4$	$4$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{4} \cdot 3^{3} \cdot 19^{3} \cdot 53^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$24168$	$48$	$0$	$1$	$1$		$0$	$165888$	$2.482983$	$436473990987119822254243753/23380189565328$	$1.02536$	$7.04541$	$[1, 1, 0, -15803194, 24173924548]$	$y^2+xy=x^3+x^2-15803194x+24173924548$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 76.12.0.?, 114.6.0.?, $\ldots$	$[]$
6042.c2	6042c3	6042.c	6042c	$4$	$4$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{4} \cdot 3^{3} \cdot 19^{12} \cdot 53 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$24168$	$48$	$0$	$1$	$1$		$0$	$165888$	$2.482983$	$148096821542276759303593/50676058386938822256$	$1.01201$	$6.12786$	$[1, 1, 0, -1102234, 284292580]$	$y^2+xy=x^3+x^2-1102234x+284292580$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 152.12.0.?, 212.12.0.?, $\ldots$	$[]$
6042.c3	6042c2	6042.c	6042c	$4$	$4$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{8} \cdot 3^{6} \cdot 19^{6} \cdot 53^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.6.0.1	2Cs	$12084$	$48$	$0$	$1$	$1$		$2$	$82944$	$2.136406$	$106578791226657105222313/24662712402544896$	$1.00247$	$6.09007$	$[1, 1, 0, -987754, 377364820]$	$y^2+xy=x^3+x^2-987754x+377364820$	2.6.0.a.1, 12.12.0-2.a.1.1, 76.12.0.?, 212.12.0.?, 228.24.0.?, $\ldots$	$[]$
6042.c4	6042c1	6042.c	6042c	$4$	$4$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ - 2^{16} \cdot 3^{12} \cdot 19^{3} \cdot 53 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$24168$	$48$	$0$	$1$	$1$		$1$	$41472$	$1.789835$	$-18035372956865677993/12661106436145152$	$0.98003$	$5.18386$	$[1, 1, 0, -54634, 7289428]$	$y^2+xy=x^3+x^2-54634x+7289428$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 76.12.0.?, 212.12.0.?, $\ldots$	$[]$
6042.d1	6042b2	6042.d	6042b	$2$	$2$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{7} \cdot 3^{6} \cdot 19^{6} \cdot 53 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$24168$	$12$	$0$	$1$	$1$		$0$	$24192$	$1.530142$	$7098888037214401273/232667098137216$	$0.96783$	$4.98553$	$[1, 1, 0, -40039, 2978485]$	$y^2+xy=x^3+x^2-40039x+2978485$	2.3.0.a.1, 228.6.0.?, 424.6.0.?, 24168.12.0.?	$[]$
6042.d2	6042b1	6042.d	6042b	$2$	$2$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{14} \cdot 3^{3} \cdot 19^{3} \cdot 53^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$24168$	$12$	$0$	$1$	$1$		$1$	$12096$	$1.183567$	$25344046984866553/8523073732608$	$0.95028$	$4.33829$	$[1, 1, 0, -6119, -121803]$	$y^2+xy=x^3+x^2-6119x-121803$	2.3.0.a.1, 114.6.0.?, 424.6.0.?, 24168.12.0.?	$[]$
6042.e1	6042f1	6042.e	6042f	$1$	$1$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{2} \cdot 3^{5} \cdot 19 \cdot 53 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$6042$	$2$	$0$	$0.137265689$	$1$		$24$	$1440$	$-0.114235$	$9759185353/978804$	$0.82801$	$2.64188$	$[1, 0, 1, -45, 100]$	$y^2+xy+y=x^3-45x+100$	6042.2.0.?	$[(2, 3), (5, 0)]$
6042.f1	6042h1	6042.f	6042h	$1$	$1$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{22} \cdot 3^{3} \cdot 19 \cdot 53 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$6042$	$2$	$0$	$1.073532604$	$1$		$4$	$9504$	$1.001835$	$48614736127265209/114038931456$	$0.94350$	$4.41311$	$[1, 0, 1, -7604, -255310]$	$y^2+xy+y=x^3-7604x-255310$	6042.2.0.?	$[(225, 2959)]$
6042.g1	6042g1	6042.g	6042g	$1$	$1$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{6} \cdot 3^{11} \cdot 19 \cdot 53 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$6042$	$2$	$0$	$0.120386511$	$1$		$10$	$5280$	$0.792506$	$3274031454654169/11416769856$	$0.92854$	$4.10324$	$[1, 0, 1, -3094, 65768]$	$y^2+xy+y=x^3-3094x+65768$	6042.2.0.?	$[(61, 293)]$
6042.h1	6042e1	6042.h	6042e	$2$	$2$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{4} \cdot 3 \cdot 19^{5} \cdot 53^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$12084$	$12$	$0$	$1$	$9$	$3$	$1$	$28800$	$1.515627$	$409329178597906017625/333857380368$	$0.98350$	$5.45123$	$[1, 0, 1, -154686, -23429408]$	$y^2+xy+y=x^3-154686x-23429408$	2.3.0.a.1, 114.6.0.?, 212.6.0.?, 12084.12.0.?	$[]$
6042.h2	6042e2	6042.h	6042e	$2$	$2$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ - 2^{2} \cdot 3^{2} \cdot 19^{10} \cdot 53 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$12084$	$12$	$0$	$1$	$9$	$3$	$0$	$57600$	$1.862202$	$-400971787828526265625/11698074419884308$	$1.01788$	$5.45451$	$[1, 0, 1, -153626, -23766064]$	$y^2+xy+y=x^3-153626x-23766064$	2.3.0.a.1, 212.6.0.?, 228.6.0.?, 12084.12.0.?	$[]$
6042.i1	6042i1	6042.i	6042i	$2$	$3$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ - 2^{9} \cdot 3^{12} \cdot 19^{2} \cdot 53^{3} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.8.0.1	3B.1.1	$1272$	$16$	$0$	$1$	$1$		$2$	$53568$	$1.868654$	$-350413509960208739017/14623786175629824$	$0.98365$	$5.44137$	$[1, 0, 1, -146877, 22421272]$	$y^2+xy+y=x^3-146877x+22421272$	3.8.0-3.a.1.2, 424.2.0.?, 1272.16.0.?	$[]$
6042.i2	6042i2	6042.i	6042i	$2$	$3$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ - 2^{27} \cdot 3^{4} \cdot 19^{6} \cdot 53 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.8.0.2	3B.1.2	$1272$	$16$	$0$	$1$	$1$		$0$	$160704$	$2.417961$	$43588367969452333114823/27107681677369933824$	$1.02657$	$5.98738$	$[1, 0, 1, 733188, 66081082]$	$y^2+xy+y=x^3+733188x+66081082$	3.8.0-3.a.1.1, 424.2.0.?, 1272.16.0.?	$[]$
6042.j1	6042j2	6042.j	6042j	$2$	$2$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{5} \cdot 3^{3} \cdot 19^{2} \cdot 53^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$24168$	$12$	$0$	$1$	$1$		$0$	$5760$	$0.760547$	$10673721082685233/876138336$	$1.01831$	$4.23897$	$[1, 1, 1, -4587, -121479]$	$y^2+xy+y=x^3+x^2-4587x-121479$	2.3.0.a.1, 24.6.0.a.1, 4028.6.0.?, 24168.12.0.?	$[]$
6042.j2	6042j1	6042.j	6042j	$2$	$2$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ - 2^{10} \cdot 3^{6} \cdot 19 \cdot 53 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$24168$	$12$	$0$	$1$	$1$		$1$	$2880$	$0.413973$	$-2105518942513/751721472$	$0.88534$	$3.31432$	$[1, 1, 1, -267, -2247]$	$y^2+xy+y=x^3+x^2-267x-2247$	2.3.0.a.1, 24.6.0.d.1, 2014.6.0.?, 24168.12.0.?	$[]$
6042.k1	6042k1	6042.k	6042k	$1$	$1$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ - 2^{5} \cdot 3^{4} \cdot 19^{2} \cdot 53 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$424$	$2$	$0$	$0.197360577$	$1$		$8$	$1600$	$0.158762$	$-4750104241/49592736$	$1.00775$	$2.89761$	$[1, 0, 0, -35, -351]$	$y^2+xy=x^3-35x-351$	424.2.0.?	$[(16, 49)]$
6042.l1	6042l1	6042.l	6042l	$1$	$1$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ - 2^{27} \cdot 3^{2} \cdot 19 \cdot 53 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$8056$	$2$	$0$	$1$	$1$		$0$	$37584$	$1.686590$	$-4275647350940405110033/1216415268864$	$1.04167$	$5.72070$	$[1, 0, 0, -338137, -75709255]$	$y^2+xy=x^3-338137x-75709255$	8056.2.0.?	$[]$
6042.m1	6042m2	6042.m	6042m	$2$	$2$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{3} \cdot 3 \cdot 19^{2} \cdot 53^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$24168$	$12$	$0$	$1$	$1$		$0$	$2304$	$0.136414$	$135559106353/24337176$	$0.85782$	$2.94409$	$[1, 0, 0, -107, 345]$	$y^2+xy=x^3-107x+345$	2.3.0.a.1, 24.6.0.a.1, 4028.6.0.?, 24168.12.0.?	$[]$
6042.m2	6042m1	6042.m	6042m	$2$	$2$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ - 2^{6} \cdot 3^{2} \cdot 19 \cdot 53 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$24168$	$12$	$0$	$1$	$1$		$1$	$1152$	$-0.210160$	$241804367/580032$	$0.81707$	$2.34876$	$[1, 0, 0, 13, 33]$	$y^2+xy=x^3+13x+33$	2.3.0.a.1, 24.6.0.d.1, 2014.6.0.?, 24168.12.0.?	$[]$
6042.n1	6042n2	6042.n	6042n	$2$	$3$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{2} \cdot 3 \cdot 19^{3} \cdot 53^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.8.0.2	3B.1.2	$6042$	$16$	$0$	$1$	$1$		$0$	$6048$	$0.659527$	$80358714342577/12253768116$	$0.90869$	$3.67743$	$[1, 0, 0, -899, -8979]$	$y^2+xy=x^3-899x-8979$	3.8.0-3.a.1.1, 6042.16.0.?	$[]$
6042.n2	6042n1	6042.n	6042n	$2$	$3$	$ 2 \cdot 3 \cdot 19 \cdot 53 $	$ 2^{6} \cdot 3^{3} \cdot 19 \cdot 53 $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.8.0.1	3B.1.1	$6042$	$16$	$0$	$1$	$1$		$2$	$2016$	$0.110221$	$1510187880817/1740096$	$0.87431$	$3.22096$	$[1, 0, 0, -239, 1401]$	$y^2+xy=x^3-239x+1401$	3.8.0-3.a.1.2, 6042.16.0.?	$[]$

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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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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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