LMFDB - Elliptic curves over $\Q$ of conductor 57475

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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 (25 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
57475.a1	57475c1	57475.a	57475c	$1$	$1$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{6} \cdot 11^{9} \cdot 19^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$5.797248914$	$1$		$0$	$1026432$	$1.777027$	$110592/361$	$0.82546$	$4.05016$	$[0, 0, 1, 33275, -5032844]$	$y^2+y=x^3+33275x-5032844$	22.2.0.a.1	$[(11011/3, 1166608/3)]$
57475.b1	57475e2	57475.b	57475e	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{10} \cdot 11^{3} \cdot 19^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$836$	$12$	$0$	$1.784129713$	$1$		$14$	$73728$	$1.120922$	$390617891/225625$	$0.94680$	$3.34275$	$[1, 0, 0, -4188, -4883]$	$y^2+xy=x^3-4188x-4883$	2.3.0.a.1, 44.6.0.a.1, 76.6.0.?, 836.12.0.?	$[(-33, 329), (92, 579)]$
57475.b2	57475e1	57475.b	57475e	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{8} \cdot 11^{3} \cdot 19 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$836$	$12$	$0$	$1.784129713$	$1$		$19$	$36864$	$0.774348$	$118370771/475$	$0.80710$	$3.23381$	$[1, 0, 0, -2813, 56992]$	$y^2+xy=x^3-2813x+56992$	2.3.0.a.1, 44.6.0.b.1, 76.6.0.?, 418.6.0.?, 836.12.0.?	$[(37, 44), (43, 105)]$
57475.c1	57475l2	57475.c	57475l	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{9} \cdot 11^{6} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$380$	$12$	$0$	$3.430934138$	$1$		$4$	$204800$	$1.677008$	$13312053/361$	$0.88614$	$4.13140$	$[1, -1, 1, -74680, -7650178]$	$y^2+xy+y=x^3-x^2-74680x-7650178$	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[(-142, 346)]$
57475.c2	57475l1	57475.c	57475l	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{9} \cdot 11^{6} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$380$	$12$	$0$	$6.861868276$	$1$		$3$	$102400$	$1.330435$	$27/19$	$1.11940$	$3.58338$	$[1, -1, 1, 945, -390178]$	$y^2+xy+y=x^3-x^2+945x-390178$	2.3.0.a.1, 20.6.0.c.1, 76.6.0.?, 190.6.0.?, 380.12.0.?	$[(910, 26993)]$
57475.d1	57475d2	57475.d	57475d	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{9} \cdot 11^{9} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4180$	$12$	$0$	$1$	$4$	$2$	$0$	$1824768$	$2.769833$	$32826402662859/45125$	$1.03490$	$5.69024$	$[1, -1, 1, -22196505, 40256346122]$	$y^2+xy+y=x^3-x^2-22196505x+40256346122$	2.3.0.a.1, 220.6.0.?, 380.6.0.?, 836.6.0.?, 4180.12.0.?	$[]$
57475.d2	57475d1	57475.d	57475d	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{12} \cdot 11^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4180$	$12$	$0$	$1$	$4$	$2$	$1$	$912384$	$2.423260$	$8230172859/296875$	$0.97938$	$4.93368$	$[1, -1, 1, -1399630, 617502372]$	$y^2+xy+y=x^3-x^2-1399630x+617502372$	2.3.0.a.1, 220.6.0.?, 380.6.0.?, 418.6.0.?, 4180.12.0.?	$[]$
57475.e1	57475j2	57475.e	57475j	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{7} \cdot 11^{8} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4180$	$12$	$0$	$4.876498982$	$1$		$0$	$368640$	$1.777622$	$3301293169/218405$	$0.81334$	$4.19392$	$[1, 1, 1, -93838, -10451594]$	$y^2+xy+y=x^3+x^2-93838x-10451594$	2.3.0.a.1, 10.6.0.a.1, 836.6.0.?, 4180.12.0.?	$[(3211/3, 29776/3)]$
57475.e2	57475j1	57475.e	57475j	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{8} \cdot 11^{7} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4180$	$12$	$0$	$2.438249491$	$1$		$3$	$184320$	$1.431049$	$24137569/5225$	$0.98391$	$3.74513$	$[1, 1, 1, -18213, 740906]$	$y^2+xy+y=x^3+x^2-18213x+740906$	2.3.0.a.1, 20.6.0.c.1, 418.6.0.?, 4180.12.0.?	$[(204, 2257)]$
57475.f1	57475g1	57475.f	57475g	$2$	$3$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{6} \cdot 11^{9} \cdot 19^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$330$	$16$	$0$	$1$	$1$		$0$	$311040$	$1.815250$	$-2258403328/480491$	$0.89836$	$4.18784$	$[0, -1, 1, -82683, -10674357]$	$y^2+y=x^3-x^2-82683x-10674357$	3.4.0.a.1, 22.2.0.a.1, 30.8.0-3.a.1.1, 66.8.0.a.1, 165.8.0.?, $\ldots$	$[]$
57475.f2	57475g2	57475.f	57475g	$2$	$3$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{6} \cdot 11^{7} \cdot 19^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$330$	$16$	$0$	$1$	$1$		$0$	$933120$	$2.364555$	$790939860992/517504691$	$1.13574$	$4.69386$	$[0, -1, 1, 582817, 61698768]$	$y^2+y=x^3-x^2+582817x+61698768$	3.4.0.a.1, 22.2.0.a.1, 30.8.0-3.a.1.2, 66.8.0.a.1, 165.8.0.?, $\ldots$	$[]$
57475.g1	57475h3	57475.g	57475h	$3$	$9$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{6} \cdot 11^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	27.36.0.1	3B	$56430$	$1296$	$43$	$1$	$1$		$0$	$437400$	$2.037106$	$-50357871050752/19$	$1.10495$	$5.07288$	$[0, -1, 1, -2327233, 1367270618]$	$y^2+y=x^3-x^2-2327233x+1367270618$	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$	$[]$
57475.g2	57475h2	57475.g	57475h	$3$	$9$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{6} \cdot 11^{6} \cdot 19^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.36.0.2	3Cs	$56430$	$1296$	$43$	$1$	$1$		$0$	$145800$	$1.487799$	$-89915392/6859$	$1.03310$	$3.87643$	$[0, -1, 1, -28233, 1951993]$	$y^2+y=x^3-x^2-28233x+1951993$	3.12.0.a.1, 9.36.0.b.1, 38.2.0.a.1, 114.24.1.?, 165.24.0.?, $\ldots$	$[]$
57475.g3	57475h1	57475.g	57475h	$3$	$9$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{6} \cdot 11^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	27.36.0.1	3B	$56430$	$1296$	$43$	$1$	$1$		$0$	$48600$	$0.938494$	$32768/19$	$1.31757$	$3.14270$	$[0, -1, 1, 2017, 868]$	$y^2+y=x^3-x^2+2017x+868$	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$	$[]$
57475.h1	57475b2	57475.h	57475b	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{10} \cdot 11^{9} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$836$	$12$	$0$	$5.564538044$	$1$		$0$	$811008$	$2.319870$	$390617891/225625$	$0.94680$	$4.65557$	$[1, 0, 1, -506751, 5992523]$	$y^2+xy+y=x^3-506751x+5992523$	2.3.0.a.1, 44.6.0.a.1, 76.6.0.?, 836.12.0.?	$[(5323/2, 323423/2)]$
57475.h2	57475b1	57475.h	57475b	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{8} \cdot 11^{9} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$836$	$12$	$0$	$2.782269022$	$4$	$2$	$3$	$405504$	$1.973295$	$118370771/475$	$0.80710$	$4.54663$	$[1, 0, 1, -340376, -76196727]$	$y^2+xy+y=x^3-340376x-76196727$	2.3.0.a.1, 44.6.0.b.1, 76.6.0.?, 418.6.0.?, 836.12.0.?	$[(-333, 666)]$
57475.i1	57475a2	57475.i	57475a	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{9} \cdot 11^{3} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4180$	$12$	$0$	$9.382399354$	$1$		$0$	$165888$	$1.570885$	$32826402662859/45125$	$1.03490$	$4.37742$	$[1, -1, 0, -183442, -30195159]$	$y^2+xy=x^3-x^2-183442x-30195159$	2.3.0.a.1, 220.6.0.?, 380.6.0.?, 836.6.0.?, 4180.12.0.?	$[(7925/4, 17831/4)]$
57475.i2	57475a1	57475.i	57475a	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{12} \cdot 11^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4180$	$12$	$0$	$4.691199677$	$1$		$3$	$82944$	$1.224310$	$8230172859/296875$	$0.97938$	$3.62086$	$[1, -1, 0, -11567, -460784]$	$y^2+xy=x^3-x^2-11567x-460784$	2.3.0.a.1, 220.6.0.?, 380.6.0.?, 418.6.0.?, 4180.12.0.?	$[(300, 4646)]$
57475.j1	57475k2	57475.j	57475k	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{3} \cdot 11^{6} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$380$	$12$	$0$	$1.841807472$	$1$		$4$	$40960$	$0.872290$	$13312053/361$	$0.88614$	$3.25025$	$[1, -1, 0, -2987, -60604]$	$y^2+xy=x^3-x^2-2987x-60604$	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[(-32, 54)]$
57475.j2	57475k1	57475.j	57475k	$2$	$2$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{3} \cdot 11^{6} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$380$	$12$	$0$	$3.683614945$	$1$		$3$	$20480$	$0.525716$	$27/19$	$1.11940$	$2.70223$	$[1, -1, 0, 38, -3129]$	$y^2+xy=x^3-x^2+38x-3129$	2.3.0.a.1, 20.6.0.c.1, 76.6.0.?, 190.6.0.?, 380.12.0.?	$[(30, 141)]$
57475.k1	57475i4	57475.k	57475i	$4$	$4$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{10} \cdot 11^{7} \cdot 19^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$8360$	$48$	$0$	$1$	$16$	$2$	$0$	$50872320$	$4.412636$	$116256292809537371612841/15216540068579856875$	$1.02754$	$7.04018$	$[1, -1, 0, -3075787292, 57757704998241]$	$y^2+xy=x^3-x^2-3075787292x+57757704998241$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 44.12.0.h.1, 152.12.0.?, $\ldots$	$[]$
57475.k2	57475i2	57475.k	57475i	$4$	$4$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{14} \cdot 11^{8} \cdot 19^{6} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$4180$	$48$	$0$	$1$	$16$	$2$	$2$	$25436160$	$4.066063$	$104859453317683374662841/2223652969140625$	$1.04825$	$7.03077$	$[1, -1, 0, -2971802917, 62355582107616]$	$y^2+xy=x^3-x^2-2971802917x+62355582107616$	2.6.0.a.1, 20.12.0-2.a.1.1, 44.12.0.a.1, 76.12.0.?, 220.24.0.?, $\ldots$	$[]$
57475.k3	57475i1	57475.k	57475i	$4$	$4$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{10} \cdot 11^{7} \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$8360$	$48$	$0$	$1$	$4$	$2$	$1$	$12718080$	$3.719490$	$104857852278310619039721/47155625$	$1.04825$	$7.03076$	$[1, -1, 0, -2971787792, 62356248560491]$	$y^2+xy=x^3-x^2-2971787792x+62356248560491$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 88.12.0.?, 152.12.0.?, $\ldots$	$[]$
57475.k4	57475i3	57475.k	57475i	$4$	$4$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{22} \cdot 11^{10} \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$8360$	$48$	$0$	$1$	$16$	$2$	$0$	$50872320$	$4.412636$	$-94256762600623910012361/15323275604248046875$	$1.02668$	$7.04363$	$[1, -1, 0, -2868060542, 66910806051491]$	$y^2+xy=x^3-x^2-2868060542x+66910806051491$	2.3.0.a.1, 4.6.0.c.1, 38.6.0.b.1, 40.12.0-4.c.1.5, 76.12.0.?, $\ldots$	$[]$
57475.l1	57475f1	57475.l	57475f	$1$	$1$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ - 5^{6} \cdot 11^{3} \cdot 19^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1$	$4$	$2$	$0$	$93312$	$0.578078$	$110592/361$	$0.82546$	$2.73734$	$[0, 0, 1, 275, 3781]$	$y^2+y=x^3+275x+3781$	22.2.0.a.1	$[]$

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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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