LMFDB - Elliptic curve search results

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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 (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	Semistable	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
1430.j2	1430i1	1430.j	1430i	$2$	$2$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$288$	$-0.168089$	$881974079/929500$	$0.83354$	$2.83502$	$[1, 1, 1, 20, -23]$	$y^2+xy+y=x^3+x^2+20x-23$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
7150.b2	7150d1	7150.b	7150d	$2$	$2$	$ 2 \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 5^{9} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$0.556562956$	$1$	$11$	$6912$	$0.636630$	$881974079/929500$	$0.83354$	$3.40899$	$[1, 0, 1, 499, -3852]$	$y^2+xy+y=x^3+499x-3852$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(12, 56)]$
11440.g2	11440w1	11440.g	11440w	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{14} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$0.487991404$	$1$	$9$	$6912$	$0.525059$	$881974079/929500$	$0.83354$	$3.09426$	$[0, 1, 0, 320, 2100]$	$y^2=x^3+x^2+320x+2100$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(10, 80)]$
12870.l2	12870n1	12870.l	12870n	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 3^{6} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$6912$	$0.381217$	$881974079/929500$	$0.83354$	$2.87333$	$[1, -1, 0, 180, 796]$	$y^2+xy=x^3-x^2+180x+796$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
15730.o2	15730n1	15730.o	15730n	$2$	$2$	$ 2 \cdot 5 \cdot 11^{2} \cdot 13 $	$ - 2^{2} \cdot 5^{3} \cdot 11^{7} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$0.702679135$	$1$	$5$	$34560$	$1.030859$	$881974079/929500$	$0.83354$	$3.62039$	$[1, 1, 0, 2418, 42464]$	$y^2+xy=x^3+x^2+2418x+42464$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(83, 866)]$
18590.h2	18590f1	18590.h	18590f	$2$	$2$	$ 2 \cdot 5 \cdot 11 \cdot 13^{2} $	$ - 2^{2} \cdot 5^{3} \cdot 11 \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$48384$	$1.114386$	$881974079/929500$	$0.83354$	$3.66083$	$[1, 1, 0, 3377, -67023]$	$y^2+xy=x^3+x^2+3377x-67023$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
45760.f2	45760i1	45760.f	45760i	$2$	$2$	$ 2^{6} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{20} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$55296$	$0.871632$	$881974079/929500$	$0.83354$	$3.08208$	$[0, 1, 0, 1279, -15521]$	$y^2=x^3+x^2+1279x-15521$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
45760.bm2	45760bc1	45760.bm	45760bc	$2$	$2$	$ 2^{6} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{20} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$55296$	$0.871632$	$881974079/929500$	$0.83354$	$3.08208$	$[0, -1, 0, 1279, 15521]$	$y^2=x^3-x^2+1279x+15521$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
57200.ci2	57200br1	57200.ci	57200br	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{14} \cdot 5^{9} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$3.217648254$	$1$	$1$	$165888$	$1.329777$	$881974079/929500$	$0.83354$	$3.52118$	$[0, -1, 0, 7992, 246512]$	$y^2=x^3-x^2+7992x+246512$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(-67/2, 2625/2)]$
64350.cv2	64350em1	64350.cv	64350em	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 3^{6} \cdot 5^{9} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$165888$	$1.185936$	$881974079/929500$	$0.83354$	$3.32782$	$[1, -1, 1, 4495, 103997]$	$y^2+xy+y=x^3-x^2+4495x+103997$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
70070.bf2	70070bg1	70070.bf	70070bg	$2$	$2$	$ 2 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 5^{3} \cdot 7^{6} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1.942165061$	$1$	$3$	$82944$	$0.804867$	$881974079/929500$	$0.83354$	$2.89257$	$[1, 0, 0, 979, 10765]$	$y^2+xy=x^3+979x+10765$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(46, 369)]$
78650.cc2	78650cp1	78650.cc	78650cp	$2$	$2$	$ 2 \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$ - 2^{2} \cdot 5^{9} \cdot 11^{7} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$829440$	$1.835577$	$881974079/929500$	$0.83354$	$3.96014$	$[1, 0, 0, 60437, 5187117]$	$y^2+xy=x^3+60437x+5187117$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
92950.cc2	92950cm1	92950.cc	92950cm	$2$	$2$	$ 2 \cdot 5^{2} \cdot 11 \cdot 13^{2} $	$ - 2^{2} \cdot 5^{9} \cdot 11 \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$12.07506410$	$1$	$1$	$1161216$	$1.919106$	$881974079/929500$	$0.83354$	$3.98992$	$[1, 0, 0, 84412, -8546708]$	$y^2+xy=x^3+84412x-8546708$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(1156444/95, 1738951182/95)]$
102960.i2	102960dl1	102960.i	102960dl	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{14} \cdot 3^{6} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$165888$	$1.074364$	$881974079/929500$	$0.83354$	$3.07631$	$[0, 0, 0, 2877, -53822]$	$y^2=x^3+2877x-53822$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
125840.t2	125840cl1	125840.t	125840cl	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11^{2} \cdot 13 $	$ - 2^{14} \cdot 5^{3} \cdot 11^{7} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$829440$	$1.724007$	$881974079/929500$	$0.83354$	$3.68762$	$[0, 1, 0, 38680, -2640332]$	$y^2=x^3+x^2+38680x-2640332$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
141570.co2	141570bc1	141570.co	141570bc	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 $	$ - 2^{2} \cdot 3^{6} \cdot 5^{3} \cdot 11^{7} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$829440$	$1.580166$	$881974079/929500$	$0.83354$	$3.50546$	$[1, -1, 1, 21757, -1124769]$	$y^2+xy+y=x^3-x^2+21757x-1124769$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
148720.g2	148720f1	148720.g	148720f	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 \cdot 13^{2} $	$ - 2^{14} \cdot 5^{3} \cdot 11 \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$1161216$	$1.807533$	$881974079/929500$	$0.83354$	$3.72005$	$[0, 1, 0, 54024, 4397524]$	$y^2=x^3+x^2+54024x+4397524$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
167310.en2	167310c1	167310.en	167310c	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} $	$ - 2^{2} \cdot 3^{6} \cdot 5^{3} \cdot 11 \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$1161216$	$1.663692$	$881974079/929500$	$0.83354$	$3.54011$	$[1, -1, 1, 30388, 1840011]$	$y^2+xy+y=x^3-x^2+30388x+1840011$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$
204490.db2	204490br1	204490.db	204490br	$2$	$2$	$ 2 \cdot 5 \cdot 11^{2} \cdot 13^{2} $	$ - 2^{2} \cdot 5^{3} \cdot 11^{7} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$32.46340980$	$1$	$1$	$5806080$	$2.313335$	$881974079/929500$	$0.83354$	$4.11953$	$[1, 1, 1, 408554, 91250479]$	$y^2+xy+y=x^3+x^2+408554x+91250479$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(1959269343487813/938551, 89682778859261303007107/938551)]$
228800.bb2	228800q1	228800.bb	228800q	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{20} \cdot 5^{9} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$5.209645286$	$1$	$3$	$1327104$	$1.676352$	$881974079/929500$	$0.83354$	$3.46263$	$[0, 1, 0, 31967, 2004063]$	$y^2=x^3+x^2+31967x+2004063$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(1217, 42952)]$
228800.fk2	228800fx1	228800.fk	228800fx	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{20} \cdot 5^{9} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$10.57350780$	$1$	$1$	$1327104$	$1.676352$	$881974079/929500$	$0.83354$	$3.46263$	$[0, -1, 0, 31967, -2004063]$	$y^2=x^3-x^2+31967x-2004063$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(226947/23, 115737492/23)]$
350350.dc2	350350dc1	350350.dc	350350dc	$2$	$2$	$ 2 \cdot 5^{2} \cdot 7^{2} \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 5^{9} \cdot 7^{6} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$3.132932005$	$1$	$3$	$1990656$	$1.609585$	$881974079/929500$	$0.83354$	$3.28431$	$[1, 1, 0, 24475, 1345625]$	$y^2+xy=x^3+x^2+24475x+1345625$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(76, 1873)]$
411840.hl2	411840hl1	411840.hl	411840hl	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{20} \cdot 3^{6} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1.652120411$	$1$	$5$	$1327104$	$1.420938$	$881974079/929500$	$0.83354$	$3.06813$	$[0, 0, 0, 11508, -430576]$	$y^2=x^3+11508x-430576$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(98, 1280)]$
411840.nd2	411840nd1	411840.nd	411840nd	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{20} \cdot 3^{6} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$2.540431193$	$1$	$5$	$1327104$	$1.420938$	$881974079/929500$	$0.83354$	$3.06813$	$[0, 0, 0, 11508, 430576]$	$y^2=x^3+11508x+430576$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[(30, 896)]$
413270.bu2	413270bu1	413270.bu	413270bu	$2$	$2$	$ 2 \cdot 5 \cdot 11 \cdot 13 \cdot 17^{2} $	$ - 2^{2} \cdot 5^{3} \cdot 11 \cdot 13^{2} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$	$1$	$1474560$	$1.248518$	$881974079/929500$	$0.83354$	$2.90731$	$[1, 0, 0, 5774, -152544]$	$y^2+xy=x^3+5774x-152544$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[ ]$

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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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