LMFDB - Elliptic curves over $\Q$ of conductor 18176

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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	Manin constant

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Results (32 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
18176.a1	18176t1	18176.a	18176t	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.3.0.1	3Nn	$1704$	$12$	$1$	$0.254577835$	$1$		$4$	$9216$	$0.332761$	$5053029696/357911$	$0.94779$	$2.91415$	$[0, 0, 0, -286, 1744]$	$y^2=x^3-286x+1744$	3.3.0.a.1, 12.6.0.d.1, 568.2.0.?, 1704.12.1.?	$[(30, 142)]$
18176.b1	18176o1	18176.b	18176o	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$568$	$2$	$0$	$0.774051314$	$1$		$10$	$2688$	$-0.421923$	$216000/71$	$0.63001$	$1.88842$	$[0, 0, 0, -10, -8]$	$y^2=x^3-10x-8$	568.2.0.?	$[(-2, 2), (-1, 1)]$
18176.c1	18176j1	18176.c	18176j	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$568$	$2$	$0$	$1.019378425$	$1$		$10$	$5376$	$-0.075349$	$216000/71$	$0.63001$	$2.31246$	$[0, 0, 0, -40, 64]$	$y^2=x^3-40x+64$	568.2.0.?	$[(0, 8), (8, 16)]$
18176.d1	18176e1	18176.d	18176e	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.3.0.1	3Nn	$1704$	$12$	$1$	$2.004060938$	$1$		$2$	$18432$	$0.679335$	$5053029696/357911$	$0.94779$	$3.33819$	$[0, 0, 0, -1144, -13952]$	$y^2=x^3-1144x-13952$	3.3.0.a.1, 12.6.0.d.1, 568.2.0.?, 1704.12.1.?	$[(-16, 16)]$
18176.e1	18176r3	18176.e	18176r	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.30.0.1	5B	$28400$	$1200$	$37$	$2.138176948$	$1$		$0$	$73600$	$1.835943$	$3922540634246430781376/71$	$1.04318$	$5.70556$	$[0, -1, 0, -2628479, 1641106963]$	$y^2=x^3-x^2-2628479x+1641106963$	5.6.0.a.1, 25.30.0.a.1, 40.12.0.bp.2, 80.24.0.?, 200.60.0.?, $\ldots$	$[(45882/7, 1/7)]$
18176.e2	18176r2	18176.e	18176r	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.1	5Cs	$28400$	$1200$	$37$	$0.427635389$	$1$		$2$	$14720$	$1.031223$	$17406197775296/1804229351$	$0.95568$	$3.74457$	$[0, -1, 0, -4319, 100435]$	$y^2=x^3-x^2-4319x+100435$	5.30.0.a.1, 40.60.0.b.1, 80.120.0.?, 568.2.0.?, 1420.60.2.?, $\ldots$	$[(26, 71)]$
18176.e3	18176r1	18176.e	18176r	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.30.0.1	5B	$28400$	$1200$	$37$	$2.138176948$	$1$		$0$	$2944$	$0.226505$	$190705121216/71$	$1.14267$	$3.28434$	$[0, -1, 0, -959, -11117]$	$y^2=x^3-x^2-959x-11117$	5.6.0.a.1, 25.30.0.a.1, 40.12.0.bp.1, 80.24.0.?, 200.60.0.?, $\ldots$	$[(-158/3, 1/3)]$
18176.f1	18176s1	18176.f	18176s	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$568$	$2$	$0$	$0.907642767$	$1$		$2$	$1024$	$-0.362942$	$1560896/71$	$0.75432$	$2.09007$	$[0, -1, 0, -19, -25]$	$y^2=x^3-x^2-19x-25$	568.2.0.?	$[(-2, 1)]$
18176.g1	18176c3	18176.g	18176c	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.30.0.1	5B	$28400$	$1200$	$37$	$22.83150950$	$1$		$0$	$147200$	$2.182514$	$3922540634246430781376/71$	$1.04318$	$6.12960$	$[0, -1, 0, -10513917, -13118341787]$	$y^2=x^3-x^2-10513917x-13118341787$	5.6.0.a.1, 25.30.0.a.1, 40.12.0.bp.2, 80.24.0.?, 200.60.0.?, $\ldots$	$[(-59144897663964/177761, 2170076923871/177761)]$
18176.g2	18176c2	18176.g	18176c	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.1	5Cs	$28400$	$1200$	$37$	$4.566301900$	$1$		$2$	$29440$	$1.377798$	$17406197775296/1804229351$	$0.95568$	$4.16860$	$[0, -1, 0, -17277, -786203]$	$y^2=x^3-x^2-17277x-786203$	5.30.0.a.1, 40.60.0.b.1, 80.120.0.?, 568.2.0.?, 1420.60.2.?, $\ldots$	$[(-92, 127)]$
18176.g3	18176c1	18176.g	18176c	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.30.0.1	5B	$28400$	$1200$	$37$	$0.913260380$	$1$		$2$	$5888$	$0.573078$	$190705121216/71$	$1.14267$	$3.70837$	$[0, -1, 0, -3837, 92773]$	$y^2=x^3-x^2-3837x+92773$	5.6.0.a.1, 25.30.0.a.1, 40.12.0.bp.1, 80.24.0.?, 200.60.0.?, $\ldots$	$[(36, 1)]$
18176.h1	18176d1	18176.h	18176d	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$568$	$2$	$0$	$0.813348670$	$1$		$2$	$2048$	$-0.016369$	$1560896/71$	$0.75432$	$2.51410$	$[0, -1, 0, -77, 277]$	$y^2=x^3-x^2-77x+277$	568.2.0.?	$[(3, 8)]$
18176.i1	18176k2	18176.i	18176k	$2$	$2$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$568$	$12$	$0$	$1$	$1$		$1$	$4352$	$0.294905$	$27000000/5041$	$1.00487$	$2.80475$	$[0, 0, 0, -200, 896]$	$y^2=x^3-200x+896$	2.3.0.a.1, 8.6.0.b.1, 284.6.0.?, 568.12.0.?	$[ ]$
18176.i2	18176k1	18176.i	18176k	$2$	$2$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$568$	$12$	$0$	$1$	$1$		$1$	$2176$	$-0.051668$	$1481544000/71$	$1.08821$	$2.78906$	$[0, 0, 0, -190, 1008]$	$y^2=x^3-190x+1008$	2.3.0.a.1, 8.6.0.c.1, 284.6.0.?, 568.12.0.?	$[ ]$
18176.j1	18176f2	18176.j	18176f	$2$	$2$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$568$	$12$	$0$	$1$	$4$	$2$	$1$	$4352$	$0.294905$	$1481544000/71$	$1.08821$	$3.21309$	$[0, 0, 0, -760, -8064]$	$y^2=x^3-760x-8064$	2.3.0.a.1, 8.6.0.c.1, 284.6.0.?, 568.12.0.?	$[ ]$
18176.j2	18176f1	18176.j	18176f	$2$	$2$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$568$	$12$	$0$	$1$	$1$		$1$	$2176$	$-0.051668$	$27000000/5041$	$1.00487$	$2.38071$	$[0, 0, 0, -50, -112]$	$y^2=x^3-50x-112$	2.3.0.a.1, 8.6.0.b.1, 284.6.0.?, 568.12.0.?	$[ ]$
18176.k1	18176p2	18176.k	18176p	$2$	$2$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$568$	$12$	$0$	$3.573914328$	$1$		$1$	$4352$	$0.294905$	$27000000/5041$	$1.00487$	$2.80475$	$[0, 0, 0, -200, -896]$	$y^2=x^3-200x-896$	2.3.0.a.1, 8.6.0.b.1, 284.6.0.?, 568.12.0.?	$[(-56/3, 280/3)]$
18176.k2	18176p1	18176.k	18176p	$2$	$2$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$568$	$12$	$0$	$7.147828656$	$1$		$1$	$2176$	$-0.051668$	$1481544000/71$	$1.08821$	$2.78906$	$[0, 0, 0, -190, -1008]$	$y^2=x^3-190x-1008$	2.3.0.a.1, 8.6.0.c.1, 284.6.0.?, 568.12.0.?	$[(1408/7, 45060/7)]$
18176.l1	18176a2	18176.l	18176a	$2$	$2$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$568$	$12$	$0$	$4.073853006$	$1$		$3$	$4352$	$0.294905$	$1481544000/71$	$1.08821$	$3.21309$	$[0, 0, 0, -760, 8064]$	$y^2=x^3-760x+8064$	2.3.0.a.1, 8.6.0.c.1, 284.6.0.?, 568.12.0.?	$[(65, 483)]$
18176.l2	18176a1	18176.l	18176a	$2$	$2$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$568$	$12$	$0$	$2.036926503$	$1$		$5$	$2176$	$-0.051668$	$27000000/5041$	$1.00487$	$2.38071$	$[0, 0, 0, -50, 112]$	$y^2=x^3-50x+112$	2.3.0.a.1, 8.6.0.b.1, 284.6.0.?, 568.12.0.?	$[(-6, 14)]$
18176.m1	18176l1	18176.m	18176l	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$568$	$2$	$0$	$0.956168554$	$1$		$6$	$1024$	$-0.362942$	$1560896/71$	$0.75432$	$2.09007$	$[0, 1, 0, -19, 25]$	$y^2=x^3+x^2-19x+25$	568.2.0.?	$[(3, 2), (0, 5)]$
18176.n1	18176b3	18176.n	18176b	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.30.0.1	5B	$28400$	$1200$	$37$	$17.29020060$	$1$		$0$	$73600$	$1.835943$	$3922540634246430781376/71$	$1.04318$	$5.70556$	$[0, 1, 0, -2628479, -1641106963]$	$y^2=x^3+x^2-2628479x-1641106963$	5.6.0.a.1, 25.30.0.a.1, 40.12.0.bp.2, 80.24.0.?, 200.60.0.?, $\ldots$	$[(-328174153423/18721, 781302524/18721)]$
18176.n2	18176b2	18176.n	18176b	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.1	5Cs	$28400$	$1200$	$37$	$3.458040121$	$1$		$2$	$14720$	$1.031223$	$17406197775296/1804229351$	$0.95568$	$3.74457$	$[0, 1, 0, -4319, -100435]$	$y^2=x^3+x^2-4319x-100435$	5.30.0.a.1, 40.60.0.b.1, 80.120.0.?, 568.2.0.?, 1420.60.2.?, $\ldots$	$[(-31, 68)]$
18176.n3	18176b1	18176.n	18176b	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.30.0.1	5B	$28400$	$1200$	$37$	$0.691608024$	$1$		$2$	$2944$	$0.226505$	$190705121216/71$	$1.14267$	$3.28434$	$[0, 1, 0, -959, 11117]$	$y^2=x^3+x^2-959x+11117$	5.6.0.a.1, 25.30.0.a.1, 40.12.0.bp.1, 80.24.0.?, 200.60.0.?, $\ldots$	$[(17, 4)]$
18176.o1	18176g1	18176.o	18176g	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$568$	$2$	$0$	$1$	$1$		$0$	$2048$	$-0.016369$	$1560896/71$	$0.75432$	$2.51410$	$[0, 1, 0, -77, -277]$	$y^2=x^3+x^2-77x-277$	568.2.0.?	$[ ]$
18176.p1	18176q3	18176.p	18176q	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.30.0.1	5B	$28400$	$1200$	$37$	$5.968677663$	$1$		$0$	$147200$	$2.182514$	$3922540634246430781376/71$	$1.04318$	$6.12960$	$[0, 1, 0, -10513917, 13118341787]$	$y^2=x^3+x^2-10513917x+13118341787$	5.6.0.a.1, 25.30.0.a.1, 40.12.0.bp.2, 80.24.0.?, 200.60.0.?, $\ldots$	$[(825469/21, 53432/21)]$
18176.p2	18176q2	18176.p	18176q	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.1	5Cs	$28400$	$1200$	$37$	$1.193735532$	$1$		$0$	$29440$	$1.377798$	$17406197775296/1804229351$	$0.95568$	$4.16860$	$[0, 1, 0, -17277, 786203]$	$y^2=x^3+x^2-17277x+786203$	5.30.0.a.1, 40.60.0.b.1, 80.120.0.?, 568.2.0.?, 1420.60.2.?, $\ldots$	$[(1453/3, 40328/3)]$
18176.p3	18176q1	18176.p	18176q	$3$	$25$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.30.0.1	5B	$28400$	$1200$	$37$	$5.968677663$	$1$		$0$	$5888$	$0.573078$	$190705121216/71$	$1.14267$	$3.70837$	$[0, 1, 0, -3837, -92773]$	$y^2=x^3+x^2-3837x-92773$	5.6.0.a.1, 25.30.0.a.1, 40.12.0.bp.1, 80.24.0.?, 200.60.0.?, $\ldots$	$[(781/3, 13096/3)]$
18176.q1	18176n1	18176.q	18176n	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.3.0.1	3Nn	$1704$	$12$	$1$	$1$	$1$		$0$	$9216$	$0.332761$	$5053029696/357911$	$0.94779$	$2.91415$	$[0, 0, 0, -286, -1744]$	$y^2=x^3-286x-1744$	3.3.0.a.1, 12.6.0.d.1, 568.2.0.?, 1704.12.1.?	$[ ]$
18176.r1	18176m1	18176.r	18176m	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$568$	$2$	$0$	$1$	$1$		$0$	$5376$	$-0.075349$	$216000/71$	$0.63001$	$2.31246$	$[0, 0, 0, -40, -64]$	$y^2=x^3-40x-64$	568.2.0.?	$[ ]$
18176.s1	18176h1	18176.s	18176h	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{9} \cdot 71 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$568$	$2$	$0$	$1$	$1$		$0$	$2688$	$-0.421923$	$216000/71$	$0.63001$	$1.88842$	$[0, 0, 0, -10, 8]$	$y^2=x^3-10x+8$	568.2.0.?	$[ ]$
18176.t1	18176i1	18176.t	18176i	$1$	$1$	$ 2^{8} \cdot 71 $	$ 2^{15} \cdot 71^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.3.0.1	3Nn	$1704$	$12$	$1$	$1$	$1$		$0$	$18432$	$0.679335$	$5053029696/357911$	$0.94779$	$3.33819$	$[0, 0, 0, -1144, 13952]$	$y^2=x^3-1144x+13952$	3.3.0.a.1, 12.6.0.d.1, 568.2.0.?, 1704.12.1.?	$[ ]$

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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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