LMFDB - Elliptic curves over $\Q$ of conductor 2475

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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	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
2475.a1	2475h3	2475.a	2475h	$3$	$25$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{6} \cdot 5^{6} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.60.0.2	5B.4.2	$1650$	$1200$	$37$	$1$	$1$	$0$	$21000$	$1.850735$	$-52893159101157376/11$	$1.09296$	$7.00734$	$[0, 0, 1, -1759575, 898379406]$	$y^2+y=x^3-1759575x+898379406$	5.12.0.a.2, 15.24.0-5.a.2.2, 22.2.0.a.1, 25.60.0.a.2, 75.120.0.?, $\ldots$	$[]$
2475.a2	2475h2	2475.a	2475h	$3$	$25$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{6} \cdot 5^{6} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.60.0.1	5Cs.4.1	$1650$	$1200$	$37$	$1$	$1$	$0$	$4200$	$1.046015$	$-122023936/161051$	$1.01300$	$4.61429$	$[0, 0, 1, -2325, 78156]$	$y^2+y=x^3-2325x+78156$	5.60.0.a.1, 15.120.0-5.a.1.2, 22.2.0.a.1, 110.120.5.?, 275.300.12.?, $\ldots$	$[]$
2475.a3	2475h1	2475.a	2475h	$3$	$25$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{6} \cdot 5^{6} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.60.0.1	5B.4.1	$1650$	$1200$	$37$	$1$	$1$	$0$	$840$	$0.241296$	$-4096/11$	$0.82546$	$3.36525$	$[0, 0, 1, -75, -594]$	$y^2+y=x^3-75x-594$	5.12.0.a.1, 15.24.0-5.a.1.2, 22.2.0.a.1, 25.60.0.a.1, 75.120.0.?, $\ldots$	$[]$
2475.b1	2475f1	2475.b	2475f	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{3} \cdot 5^{4} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$132$	$2$	$0$	$0.117397198$	$1$	$8$	$192$	$-0.307781$	$-675/11$	$1.13667$	$2.51102$	$[1, -1, 1, -5, 22]$	$y^2+xy+y=x^3-x^2-5x+22$	132.2.0.?	$[(4, 5)]$
2475.c1	2475d2	2475.c	2475d	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{9} \cdot 5^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$	$0$	$1920$	$0.865335$	$19034163/121$	$0.94120$	$4.64626$	$[1, -1, 1, -3755, -87128]$	$y^2+xy+y=x^3-x^2-3755x-87128$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.?	$[]$
2475.c2	2475d1	2475.c	2475d	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{9} \cdot 5^{6} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$	$1$	$960$	$0.518761$	$19683/11$	$1.13667$	$3.76653$	$[1, -1, 1, -380, 622]$	$y^2+xy+y=x^3-x^2-380x+622$	2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.?	$[]$
2475.d1	2475b1	2475.d	2475b	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{9} \cdot 5^{10} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$132$	$2$	$0$	$3.114581138$	$1$	$2$	$2880$	$1.046244$	$-675/11$	$1.13667$	$4.59040$	$[1, -1, 1, -1055, -70928]$	$y^2+xy+y=x^3-x^2-1055x-70928$	132.2.0.?	$[(88, 671)]$
2475.e1	2475k1	2475.e	2475k	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{9} \cdot 5^{8} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$6$	$16$	$0$	$1$	$1$	$0$	$2880$	$1.052814$	$-56197120/3267$	$0.94162$	$4.78722$	$[0, 0, 1, -5250, -153594]$	$y^2+y=x^3-5250x-153594$	3.8.0-3.a.1.1, 6.16.0-6.b.1.1	$[]$
2475.e2	2475k2	2475.e	2475k	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{7} \cdot 5^{8} \cdot 11^{6} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$6$	$16$	$0$	$1$	$1$	$2$	$8640$	$1.602121$	$8990228480/5314683$	$1.15904$	$5.42444$	$[0, 0, 1, 28500, -271719]$	$y^2+y=x^3+28500x-271719$	3.8.0-3.a.1.2, 6.16.0-6.b.1.2	$[]$
2475.f1	2475i1	2475.f	2475i	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{9} \cdot 5^{2} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$30$	$16$	$0$	$0.553485365$	$1$	$4$	$576$	$0.248095$	$-56197120/3267$	$0.94162$	$3.55140$	$[0, 0, 1, -210, -1229]$	$y^2+y=x^3-210x-1229$	3.4.0.a.1, 6.8.0.b.1, 15.8.0-3.a.1.1, 30.16.0-6.b.1.1	$[(31, 148)]$
2475.f2	2475i2	2475.f	2475i	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{7} \cdot 5^{2} \cdot 11^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$30$	$16$	$0$	$0.184495121$	$1$	$4$	$1728$	$0.797401$	$8990228480/5314683$	$1.15904$	$4.18863$	$[0, 0, 1, 1140, -2174]$	$y^2+y=x^3+1140x-2174$	3.4.0.a.1, 6.8.0.b.1, 15.8.0-3.a.1.2, 30.16.0-6.b.1.2	$[(4, 49)]$
2475.g1	2475g3	2475.g	2475g	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{9} \cdot 5^{6} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1$	$1$	$0$	$6144$	$1.341393$	$347873904937/395307$	$1.00913$	$5.48035$	$[1, -1, 0, -32967, -2293434]$	$y^2+xy=x^3-x^2-32967x-2293434$	2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 20.12.0-4.c.1.1, 60.24.0-12.h.1.1, $\ldots$	$[]$
2475.g2	2475g2	2475.g	2475g	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{12} \cdot 5^{6} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$660$	$48$	$0$	$1$	$1$	$2$	$3072$	$0.994820$	$169112377/88209$	$1.00669$	$4.50402$	$[1, -1, 0, -2592, -15309]$	$y^2+xy=x^3-x^2-2592x-15309$	2.6.0.a.1, 12.12.0.a.1, 20.12.0-2.a.1.1, 44.12.0.b.1, 60.24.0-12.a.1.2, $\ldots$	$[]$
2475.g3	2475g1	2475.g	2475g	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{9} \cdot 5^{6} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1$	$1$	$1$	$1536$	$0.648246$	$30664297/297$	$1.09706$	$4.28550$	$[1, -1, 0, -1467, 21816]$	$y^2+xy=x^3-x^2-1467x+21816$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.ba.1, 66.6.0.a.1, $\ldots$	$[]$
2475.g4	2475g4	2475.g	2475g	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{18} \cdot 5^{6} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1$	$1$	$0$	$6144$	$1.341393$	$9090072503/5845851$	$1.03763$	$5.01392$	$[1, -1, 0, 9783, -126684]$	$y^2+xy=x^3-x^2+9783x-126684$	2.3.0.a.1, 4.6.0.c.1, 22.6.0.a.1, 24.12.0.ba.1, 40.12.0-4.c.1.5, $\ldots$	$[]$
2475.h1	2475e1	2475.h	2475e	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{9} \cdot 5^{4} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$132$	$2$	$0$	$1$	$1$	$0$	$576$	$0.241525$	$-675/11$	$1.13667$	$3.35459$	$[1, -1, 0, -42, -559]$	$y^2+xy=x^3-x^2-42x-559$	132.2.0.?	$[]$
2475.i1	2475j3	2475.i	2475j	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{6} \cdot 5^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1320$	$48$	$0$	$4.314990037$	$1$	$0$	$3072$	$1.068359$	$22930509321/6875$	$1.07717$	$5.13233$	$[1, -1, 0, -13317, -588034]$	$y^2+xy=x^3-x^2-13317x-588034$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0.z.1, 44.12.0.h.1, $\ldots$	$[(-265/2, 363/2)]$
2475.i2	2475j4	2475.i	2475j	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{6} \cdot 5^{7} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1.078747509$	$1$	$4$	$3072$	$1.068359$	$2749884201/73205$	$0.94591$	$4.86091$	$[1, -1, 0, -6567, 201716]$	$y^2+xy=x^3-x^2-6567x+201716$	2.3.0.a.1, 4.6.0.c.1, 10.6.0.a.1, 12.12.0-4.c.1.1, 20.12.0.g.1, $\ldots$	$[(28, 184)]$
2475.i3	2475j2	2475.i	2475j	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{6} \cdot 5^{8} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$660$	$48$	$0$	$2.157495018$	$1$	$6$	$1536$	$0.721786$	$8120601/3025$	$1.05560$	$4.11546$	$[1, -1, 0, -942, -6409]$	$y^2+xy=x^3-x^2-942x-6409$	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.b.1, 44.12.0.a.1, 60.24.0-20.b.1.2, $\ldots$	$[(-10, 49)]$
2475.i4	2475j1	2475.i	2475j	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{6} \cdot 5^{7} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1320$	$48$	$0$	$4.314990037$	$1$	$3$	$768$	$0.375213$	$59319/55$	$0.79207$	$3.48592$	$[1, -1, 0, 183, -784]$	$y^2+xy=x^3-x^2+183x-784$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.z.1, 88.12.0.?, $\ldots$	$[(68, 534)]$
2475.j1	2475a2	2475.j	2475a	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{3} \cdot 5^{6} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$0.984594131$	$1$	$4$	$640$	$0.316029$	$19034163/121$	$0.94120$	$3.80269$	$[1, -1, 0, -417, 3366]$	$y^2+xy=x^3-x^2-417x+3366$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.?	$[(10, 6)]$
2475.j2	2475a1	2475.j	2475a	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ 3^{3} \cdot 5^{6} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1.969188262$	$1$	$3$	$320$	$-0.030545$	$19683/11$	$1.13667$	$2.92296$	$[1, -1, 0, -42, -9]$	$y^2+xy=x^3-x^2-42x-9$	2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.?	$[(-2, 9)]$
2475.k1	2475c1	2475.k	2475c	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 11 $	$ - 3^{3} \cdot 5^{10} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$132$	$2$	$0$	$1$	$1$	$0$	$960$	$0.496938$	$-675/11$	$1.13667$	$3.74683$	$[1, -1, 0, -117, 2666]$	$y^2+xy=x^3-x^2-117x+2666$	132.2.0.?	$[]$

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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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