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	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.e1	1430k1	1430.e	1430k	$1$	$1$	$ 2 \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{13} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$440$	$2$	$0$	$0.009739866$	$1$	$28$	$6240$	$1.138571$	$-3158470573163361/5758438400000$	$0.98240$	$5.10804$	$[1, -1, 1, -3057, 133281]$	$y^2+xy+y=x^3-x^2-3057x+133281$	440.2.0.?	$[(591, 14004)]$
7150.n1	7150j1	7150.n	7150j	$1$	$1$	$ 2 \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{13} \cdot 5^{11} \cdot 11^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$149760$	$1.943291$	$-3158470573163361/5758438400000$	$0.98240$	$5.26979$	$[1, -1, 0, -76417, 16583741]$	$y^2+xy=x^3-x^2-76417x+16583741$	440.2.0.?	$[ ]$
11440.w1	11440p1	11440.w	11440p	$1$	$1$	$ 2^{4} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{25} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$149760$	$1.831718$	$-3158470573163361/5758438400000$	$0.98240$	$4.86147$	$[0, 0, 0, -48907, -8481094]$	$y^2=x^3-48907x-8481094$	440.2.0.?	$[ ]$
12870.d1	12870l1	12870.d	12870l	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$7.479227878$	$1$	$2$	$87360$	$1.687878$	$-3158470573163361/5758438400000$	$0.98240$	$4.61855$	$[1, -1, 0, -27510, -3571084]$	$y^2+xy=x^3-x^2-27510x-3571084$	440.2.0.?	$[(6275, 493729)]$
15730.a1	15730o1	15730.a	15730o	$1$	$1$	$ 2 \cdot 5 \cdot 11^{2} \cdot 13 $	$ - 2^{13} \cdot 5^{5} \cdot 11^{9} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$0.718710175$	$1$	$4$	$748800$	$2.337521$	$-3158470573163361/5758438400000$	$0.98240$	$5.32937$	$[1, -1, 0, -369859, -176287787]$	$y^2+xy=x^3-x^2-369859x-176287787$	440.2.0.?	$[(1367, 42574)]$
18590.a1	18590d1	18590.a	18590d	$1$	$1$	$ 2 \cdot 5 \cdot 11 \cdot 13^{2} $	$ - 2^{13} \cdot 5^{5} \cdot 11^{3} \cdot 13^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$5.874798267$	$1$	$0$	$1048320$	$2.421047$	$-3158470573163361/5758438400000$	$0.98240$	$5.34077$	$[1, -1, 0, -516580, 291269200]$	$y^2+xy=x^3-x^2-516580x+291269200$	440.2.0.?	$[(-1273/2, 165879/2)]$
45760.b1	45760bk1	45760.b	45760bk	$1$	$1$	$ 2^{6} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{31} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1.246646209$	$1$	$4$	$1198080$	$2.178291$	$-3158470573163361/5758438400000$	$0.98240$	$4.62100$	$[0, 0, 0, -195628, -67848752]$	$y^2=x^3-195628x-67848752$	440.2.0.?	$[(4426, 292864)]$
45760.by1	45760b1	45760.by	45760b	$1$	$1$	$ 2^{6} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{31} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$4.628746013$	$1$	$0$	$1198080$	$2.178291$	$-3158470573163361/5758438400000$	$0.98240$	$4.62100$	$[0, 0, 0, -195628, 67848752]$	$y^2=x^3-195628x+67848752$	440.2.0.?	$[(-5018/3, 51200/3)]$
57200.b1	57200bg1	57200.b	57200bg	$1$	$1$	$ 2^{4} \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{25} \cdot 5^{11} \cdot 11^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$3594240$	$2.636436$	$-3158470573163361/5758438400000$	$0.98240$	$5.02875$	$[0, 0, 0, -1222675, -1060136750]$	$y^2=x^3-1222675x-1060136750$	440.2.0.?	$[ ]$
64350.ev1	64350dn1	64350.ev	64350dn	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 5^{11} \cdot 11^{3} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1.311474998$	$1$	$4$	$2096640$	$2.492596$	$-3158470573163361/5758438400000$	$0.98240$	$4.81936$	$[1, -1, 1, -687755, -447073253]$	$y^2+xy+y=x^3-x^2-687755x-447073253$	440.2.0.?	$[(4139, 257930)]$
70070.cl1	70070bq1	70070.cl	70070bq	$1$	$1$	$ 2 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 $	$ - 2^{13} \cdot 5^{5} \cdot 7^{6} \cdot 11^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$2059200$	$2.111526$	$-3158470573163361/5758438400000$	$0.98240$	$4.37272$	$[1, -1, 1, -149778, -45415919]$	$y^2+xy+y=x^3-x^2-149778x-45415919$	440.2.0.?	$[ ]$
78650.di1	78650cr1	78650.di	78650cr	$1$	$1$	$ 2 \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$ - 2^{13} \cdot 5^{11} \cdot 11^{9} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$17971200$	$3.142239$	$-3158470573163361/5758438400000$	$0.98240$	$5.42512$	$[1, -1, 1, -9246480, -22045219853]$	$y^2+xy+y=x^3-x^2-9246480x-22045219853$	440.2.0.?	$[ ]$
92950.da1	92950bx1	92950.da	92950bx	$1$	$1$	$ 2 \cdot 5^{2} \cdot 11 \cdot 13^{2} $	$ - 2^{13} \cdot 5^{11} \cdot 11^{3} \cdot 13^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$25159680$	$3.225765$	$-3158470573163361/5758438400000$	$0.98240$	$5.43351$	$[1, -1, 1, -12914505, 36395735497]$	$y^2+xy+y=x^3-x^2-12914505x+36395735497$	440.2.0.?	$[ ]$
102960.cd1	102960dx1	102960.cd	102960dx	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{25} \cdot 3^{6} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$3.247101164$	$1$	$2$	$2096640$	$2.381023$	$-3158470573163361/5758438400000$	$0.98240$	$4.50711$	$[0, 0, 0, -440163, 228989538]$	$y^2=x^3-440163x+228989538$	440.2.0.?	$[(511, 11726)]$
125840.cr1	125840cm1	125840.cr	125840cm	$1$	$1$	$ 2^{4} \cdot 5 \cdot 11^{2} \cdot 13 $	$ - 2^{25} \cdot 5^{5} \cdot 11^{9} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$17971200$	$3.030666$	$-3158470573163361/5758438400000$	$0.98240$	$5.09396$	$[0, 0, 0, -5917747, 11288336114]$	$y^2=x^3-5917747x+11288336114$	440.2.0.?	$[ ]$
141570.do1	141570bz1	141570.do	141570bz	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 5^{5} \cdot 11^{9} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$10483200$	$2.886826$	$-3158470573163361/5758438400000$	$0.98240$	$4.89784$	$[1, -1, 1, -3328733, 4763098981]$	$y^2+xy+y=x^3-x^2-3328733x+4763098981$	440.2.0.?	$[ ]$
148720.ca1	148720bd1	148720.ca	148720bd	$1$	$1$	$ 2^{4} \cdot 5 \cdot 11 \cdot 13^{2} $	$ - 2^{25} \cdot 5^{5} \cdot 11^{3} \cdot 13^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$22.89186266$	$1$	$0$	$25159680$	$3.114193$	$-3158470573163361/5758438400000$	$0.98240$	$5.10667$	$[0, 0, 0, -8265283, -18632963518]$	$y^2=x^3-8265283x-18632963518$	440.2.0.?	$[(909606012991/10503, 797553617328173134/10503)]$
167310.fp1	167310s1	167310.fp	167310s	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} $	$ - 2^{13} \cdot 3^{6} \cdot 5^{5} \cdot 11^{3} \cdot 13^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$0.843043110$	$1$	$4$	$14676480$	$2.970352$	$-3158470573163361/5758438400000$	$0.98240$	$4.91315$	$[1, -1, 1, -4649222, -7859619179]$	$y^2+xy+y=x^3-x^2-4649222x-7859619179$	440.2.0.?	$[(5561, 369019)]$
204490.bp1	204490b1	204490.bp	204490b	$1$	$1$	$ 2 \cdot 5 \cdot 11^{2} \cdot 13^{2} $	$ - 2^{13} \cdot 5^{5} \cdot 11^{9} \cdot 13^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$2.580324165$	$1$	$4$	$125798400$	$3.619995$	$-3158470573163361/5758438400000$	$0.98240$	$5.47004$	$[1, -1, 1, -62506203, -387491786613]$	$y^2+xy+y=x^3-x^2-62506203x-387491786613$	440.2.0.?	$[(10475, 321946)]$
228800.d1	228800dm1	228800.d	228800dm	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{31} \cdot 5^{11} \cdot 11^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$28753920$	$2.983009$	$-3158470573163361/5758438400000$	$0.98240$	$4.80085$	$[0, 0, 0, -4890700, 8481094000]$	$y^2=x^3-4890700x+8481094000$	440.2.0.?	$[ ]$
228800.gi1	228800dk1	228800.gi	228800dk	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 13 $	$ - 2^{31} \cdot 5^{11} \cdot 11^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$28753920$	$2.983009$	$-3158470573163361/5758438400000$	$0.98240$	$4.80085$	$[0, 0, 0, -4890700, -8481094000]$	$y^2=x^3-4890700x-8481094000$	440.2.0.?	$[ ]$
350350.e1	350350e1	350350.e	350350e	$1$	$1$	$ 2 \cdot 5^{2} \cdot 7^{2} \cdot 11 \cdot 13 $	$ - 2^{13} \cdot 5^{11} \cdot 7^{6} \cdot 11^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$49420800$	$2.916245$	$-3158470573163361/5758438400000$	$0.98240$	$4.57786$	$[1, -1, 0, -3744442, -5680734284]$	$y^2+xy=x^3-x^2-3744442x-5680734284$	440.2.0.?	$[ ]$
411840.ib1	411840ib1	411840.ib	411840ib	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{31} \cdot 3^{6} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$16773120$	$2.727596$	$-3158470573163361/5758438400000$	$0.98240$	$4.34551$	$[0, 0, 0, -1760652, -1831916304]$	$y^2=x^3-1760652x-1831916304$	440.2.0.?	$[ ]$
411840.mu1	411840mu1	411840.mu	411840mu	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{31} \cdot 3^{6} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$1$	$1$	$0$	$16773120$	$2.727596$	$-3158470573163361/5758438400000$	$0.98240$	$4.34551$	$[0, 0, 0, -1760652, 1831916304]$	$y^2=x^3-1760652x+1831916304$	440.2.0.?	$[ ]$
413270.db1	413270db1	413270.db	413270db	$1$	$1$	$ 2 \cdot 5 \cdot 11 \cdot 13 \cdot 17^{2} $	$ - 2^{13} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} \cdot 17^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$440$	$2$	$0$	$6.478393155$	$1$	$0$	$32248320$	$2.555180$	$-3158470573163361/5758438400000$	$0.98240$	$4.18435$	$[1, -1, 1, -883383, 651277327]$	$y^2+xy+y=x^3-x^2-883383x+651277327$	440.2.0.?	$[(6355/3, 516226/3)]$

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Elliptic 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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