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

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Results (27 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
2310.j4	2310k1	2310.j	2310k	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$3080$	$48$	$0$	$0.481315981$	$1$	$9$	$1536$	$0.354229$	$788632918919/475398000$	$0.94654$	$3.53693$	$[1, 0, 1, 192, -194]$	$y^2+xy+y=x^3+192x-194$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 44.12.0-4.c.1.2, 56.12.0-4.c.1.4, $\ldots$	$[(5, 27)]$
6930.t4	6930z1	6930.t	6930z	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{8} \cdot 5^{3} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$12288$	$0.903535$	$788632918919/475398000$	$0.94654$	$3.84291$	$[1, -1, 1, 1732, 5231]$	$y^2+xy+y=x^3-x^2+1732x+5231$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 110.6.0.?, 132.12.0.?, $\ldots$	$[]$
11550.bw4	11550bs1	11550.bw	11550bs	$4$	$4$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{2} \cdot 5^{9} \cdot 7^{4} \cdot 11 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.7	2B	$3080$	$48$	$0$	$1.829134848$	$1$	$11$	$36864$	$1.158947$	$788632918919/475398000$	$0.94654$	$3.96071$	$[1, 1, 1, 4812, -24219]$	$y^2+xy+y=x^3+x^2+4812x-24219$	2.3.0.a.1, 4.12.0-4.c.1.1, 110.6.0.?, 220.24.0.?, 280.24.0.?, $\ldots$	$[(19, 263)]$
16170.g4	16170g1	16170.g	16170g	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{2} \cdot 5^{3} \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.12	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$73728$	$1.327185$	$788632918919/475398000$	$0.94654$	$4.03151$	$[1, 1, 0, 9432, 75888]$	$y^2+xy=x^3+x^2+9432x+75888$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 110.6.0.?, 140.12.0.?, $\ldots$	$[]$
18480.bo4	18480cl1	18480.bo	18480cl	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$3080$	$48$	$0$	$0.358054608$	$1$	$11$	$36864$	$1.047377$	$788632918919/475398000$	$0.94654$	$3.63495$	$[0, -1, 0, 3080, 12400]$	$y^2=x^3-x^2+3080x+12400$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 44.12.0-4.c.1.1, 56.12.0-4.c.1.4, $\ldots$	$[(10, 210)]$
25410.cy4	25410cy1	25410.cy	25410cy	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.7	2B	$3080$	$48$	$0$	$1$	$1$	$3$	$184320$	$1.553177$	$788632918919/475398000$	$0.94654$	$4.11923$	$[1, 0, 0, 23290, 281172]$	$y^2+xy=x^3+23290x+281172$	2.3.0.a.1, 4.12.0-4.c.1.1, 110.6.0.?, 220.24.0.?, 280.24.0.?, $\ldots$	$[]$
34650.cj4	34650bn1	34650.cj	34650bn	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{8} \cdot 5^{9} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$294912$	$1.708254$	$788632918919/475398000$	$0.94654$	$4.17504$	$[1, -1, 0, 43308, 697216]$	$y^2+xy=x^3-x^2+43308x+697216$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 110.6.0.?, 220.12.0.?, $\ldots$	$[]$
48510.ek4	48510ej1	48510.ek	48510ej	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{8} \cdot 5^{3} \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$589824$	$1.876490$	$788632918919/475398000$	$0.94654$	$4.23195$	$[1, -1, 1, 84883, -1964091]$	$y^2+xy+y=x^3-x^2+84883x-1964091$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 110.6.0.?, 220.12.0.?, $\ldots$	$[]$
55440.bm4	55440do1	55440.bm	55440do	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3^{8} \cdot 5^{3} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$294912$	$1.596682$	$788632918919/475398000$	$0.94654$	$3.87282$	$[0, 0, 0, 27717, -362518]$	$y^2=x^3+27717x-362518$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.1, 110.6.0.?, 132.12.0.?, $\ldots$	$[]$
73920.ba4	73920j1	73920.ba	73920j	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{22} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$294912$	$1.393950$	$788632918919/475398000$	$0.94654$	$3.55643$	$[0, -1, 0, 12319, -111519]$	$y^2=x^3-x^2+12319x-111519$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.2, 56.12.0-4.c.1.5, 88.12.0.?, $\ldots$	$[]$
73920.fq4	73920gu1	73920.fq	73920gu	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{22} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$294912$	$1.393950$	$788632918919/475398000$	$0.94654$	$3.55643$	$[0, 1, 0, 12319, 111519]$	$y^2=x^3+x^2+12319x+111519$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.1, 56.12.0-4.c.1.5, 88.12.0.?, $\ldots$	$[]$
76230.bd4	76230bk1	76230.bd	76230bk	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{8} \cdot 5^{3} \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$1474560$	$2.102482$	$788632918919/475398000$	$0.94654$	$4.30303$	$[1, -1, 0, 209610, -7591644]$	$y^2+xy=x^3-x^2+209610x-7591644$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 110.6.0.?, 220.12.0.?, $\ldots$	$[]$
80850.fm4	80850gh1	80850.fm	80850gh	$4$	$4$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{2} \cdot 5^{9} \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$1769472$	$2.131905$	$788632918919/475398000$	$0.94654$	$4.31187$	$[1, 0, 0, 235787, 9014417]$	$y^2+xy=x^3+235787x+9014417$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 40.12.0-4.c.1.4, 88.12.0.?, $\ldots$	$[]$
92400.go4	92400gs1	92400.go	92400gs	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3^{2} \cdot 5^{9} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.8	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$884736$	$1.852095$	$788632918919/475398000$	$0.94654$	$3.96785$	$[0, 1, 0, 76992, 1703988]$	$y^2=x^3+x^2+76992x+1703988$	2.3.0.a.1, 4.12.0-4.c.1.2, 110.6.0.?, 220.24.0.?, 280.24.0.?, $\ldots$	$[]$
127050.b4	127050n1	127050.b	127050n	$4$	$4$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{2} \cdot 5^{9} \cdot 7^{4} \cdot 11^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1.587026815$	$1$	$21$	$4423680$	$2.357895$	$788632918919/475398000$	$0.94654$	$4.37680$	$[1, 1, 0, 582250, 35146500]$	$y^2+xy=x^3+x^2+582250x+35146500$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 44.12.0-4.c.1.2, 56.12.0-4.c.1.6, $\ldots$	$[(1920, 89790), (920, 36290)]$
129360.fs4	129360gx1	129360.fs	129360gx	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{16} \cdot 3^{2} \cdot 5^{3} \cdot 7^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.12	2B	$3080$	$48$	$0$	$6.098626665$	$1$	$3$	$1769472$	$2.020332$	$788632918919/475398000$	$0.94654$	$4.02594$	$[0, 1, 0, 150904, -4555020]$	$y^2=x^3+x^2+150904x-4555020$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 110.6.0.?, 140.12.0.?, $\ldots$	$[(21639, 3183726)]$
177870.el4	177870dn1	177870.el	177870dn	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{2} $	$ - 2^{4} \cdot 3^{2} \cdot 5^{3} \cdot 7^{10} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$8847360$	$2.526131$	$788632918919/475398000$	$0.94654$	$4.42197$	$[1, 1, 1, 1141209, -95300787]$	$y^2+xy+y=x^3+x^2+1141209x-95300787$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 40.12.0-4.c.1.6, 88.12.0.?, $\ldots$	$[]$
203280.cx4	203280da1	203280.cx	203280da	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.8	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$4423680$	$2.246323$	$788632918919/475398000$	$0.94654$	$4.09895$	$[0, -1, 0, 372640, -17995008]$	$y^2=x^3-x^2+372640x-17995008$	2.3.0.a.1, 4.12.0-4.c.1.2, 110.6.0.?, 220.24.0.?, 280.24.0.?, $\ldots$	$[]$
221760.hw4	221760kf1	221760.hw	221760kf	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{22} \cdot 3^{8} \cdot 5^{3} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$3.230899096$	$1$	$3$	$2359296$	$1.943256$	$788632918919/475398000$	$0.94654$	$3.77452$	$[0, 0, 0, 110868, 2900144]$	$y^2=x^3+110868x+2900144$	2.3.0.a.1, 4.6.0.c.1, 110.6.0.?, 120.12.0.?, 168.12.0.?, $\ldots$	$[(998, 33280)]$
221760.nw4	221760r1	221760.nw	221760r	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{22} \cdot 3^{8} \cdot 5^{3} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$2359296$	$1.943256$	$788632918919/475398000$	$0.94654$	$3.77452$	$[0, 0, 0, 110868, -2900144]$	$y^2=x^3+110868x-2900144$	2.3.0.a.1, 4.6.0.c.1, 110.6.0.?, 120.12.0.?, 168.12.0.?, $\ldots$	$[]$
242550.dy4	242550dy1	242550.dy	242550dy	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{8} \cdot 5^{9} \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$14155776$	$2.681210$	$788632918919/475398000$	$0.94654$	$4.46145$	$[1, -1, 0, 2122083, -243389259]$	$y^2+xy=x^3-x^2+2122083x-243389259$	2.3.0.a.1, 4.6.0.c.1, 84.12.0.?, 110.6.0.?, 120.12.0.?, $\ldots$	$[]$
277200.di4	277200di1	277200.di	277200di	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3^{8} \cdot 5^{9} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$7.882208762$	$1$	$1$	$7077888$	$2.401402$	$788632918919/475398000$	$0.94654$	$4.14599$	$[0, 0, 0, 692925, -45314750]$	$y^2=x^3+692925x-45314750$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 110.6.0.?, 220.12.0.?, $\ldots$	$[(16969/3, 2409472/3)]$
369600.h4	369600h1	369600.h	369600h	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{22} \cdot 3^{2} \cdot 5^{9} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.7	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$7077888$	$2.198669$	$788632918919/475398000$	$0.94654$	$3.86320$	$[0, -1, 0, 307967, 13323937]$	$y^2=x^3-x^2+307967x+13323937$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 110.6.0.?, 220.12.0.?, $\ldots$	$[]$
369600.ur4	369600ur1	369600.ur	369600ur	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{22} \cdot 3^{2} \cdot 5^{9} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.8	2B	$3080$	$48$	$0$	$1$	$1$	$1$	$7077888$	$2.198669$	$788632918919/475398000$	$0.94654$	$3.86320$	$[0, 1, 0, 307967, -13323937]$	$y^2=x^3+x^2+307967x-13323937$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 110.6.0.?, 220.12.0.?, $\ldots$	$[]$
381150.ip4	381150ip1	381150.ip	381150ip	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{8} \cdot 5^{9} \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$	$1$	$35389440$	$2.907200$	$788632918919/475398000$	$0.94654$	$4.51556$	$[1, -1, 1, 5240245, -943715253]$	$y^2+xy+y=x^3-x^2+5240245x-943715253$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 110.6.0.?, 132.12.0.?, $\ldots$	$[]$
388080.ll4	388080ll1	388080.ll	388080ll	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{16} \cdot 3^{8} \cdot 5^{3} \cdot 7^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$9240$	$48$	$0$	$4.117946117$	$1$	$5$	$14155776$	$2.569637$	$788632918919/475398000$	$0.94654$	$4.19447$	$[0, 0, 0, 1358133, 124343674]$	$y^2=x^3+1358133x+124343674$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 110.6.0.?, 220.12.0.?, $\ldots$	$[(485, 29952)]$
390390.eh4	390390eh1	390390.eh	390390eh	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} $	$ - 2^{4} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} \cdot 11 \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$40040$	$48$	$0$	$2.084084417$	$1$	$3$	$2949120$	$1.636703$	$788632918919/475398000$	$0.94654$	$3.32300$	$[1, 0, 0, 32529, -458199]$	$y^2+xy=x^3+32529x-458199$	2.3.0.a.1, 4.6.0.c.1, 110.6.0.?, 220.12.0.?, 260.12.0.?, $\ldots$	$[(1470, 56049)]$

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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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Results (27 matches)

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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