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 (20 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
3366.h2	3366a1	3366.h	3366a	$2$	$2$	$ 2 \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{2} \cdot 3^{9} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.850748569$	$1$		$7$	$1920$	$0.357165$	$170953875/12716$	$1.00324$	$3.55162$	$[1, -1, 0, -312, 2060]$	$y^2+xy=x^3-x^2-312x+2060$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(7, 10)]$
3366.o2	3366l1	3366.o	3366l	$2$	$2$	$ 2 \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{2} \cdot 3^{3} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$640$	$-0.192141$	$170953875/12716$	$1.00324$	$2.73999$	$[1, -1, 1, -35, -65]$	$y^2+xy+y=x^3-x^2-35x-65$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
26928.w2	26928x1	26928.w	26928x	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{14} \cdot 3^{3} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.778107064$	$1$		$9$	$15360$	$0.501006$	$170953875/12716$	$1.00324$	$2.99684$	$[0, 0, 0, -555, 4698]$	$y^2=x^3-555x+4698$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(7, 34)]$
26928.x2	26928z1	26928.x	26928z	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{14} \cdot 3^{9} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.116451407$	$1$		$3$	$46080$	$1.050312$	$170953875/12716$	$1.00324$	$3.64302$	$[0, 0, 0, -4995, -126846]$	$y^2=x^3-4995x-126846$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(-47, 64)]$
37026.h2	37026c1	37026.h	37026c	$2$	$2$	$ 2 \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{2} \cdot 3^{3} \cdot 11^{7} \cdot 17^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.844516040$	$1$		$21$	$76800$	$1.006807$	$170953875/12716$	$1.00324$	$3.48311$	$[1, -1, 0, -4197, 98753]$	$y^2+xy=x^3-x^2-4197x+98753$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(-8, 367), (62, 241)]$
37026.be2	37026v1	37026.be	37026v	$2$	$2$	$ 2 \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{2} \cdot 3^{9} \cdot 11^{7} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$230400$	$1.556112$	$170953875/12716$	$1.00324$	$4.10973$	$[1, -1, 1, -37775, -2628557]$	$y^2+xy+y=x^3-x^2-37775x-2628557$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
57222.j2	57222b1	57222.j	57222b	$2$	$2$	$ 2 \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{2} \cdot 3^{9} \cdot 11 \cdot 17^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$552960$	$1.773771$	$170953875/12716$	$1.00324$	$4.18484$	$[1, -1, 0, -90222, 9759968]$	$y^2+xy=x^3-x^2-90222x+9759968$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
57222.bl2	57222be1	57222.bl	57222be	$2$	$2$	$ 2 \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{2} \cdot 3^{3} \cdot 11 \cdot 17^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$184320$	$1.224466$	$170953875/12716$	$1.00324$	$3.58312$	$[1, -1, 1, -10025, -358139]$	$y^2+xy+y=x^3-x^2-10025x-358139$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
84150.k2	84150p1	84150.k	84150p	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{2} \cdot 3^{3} \cdot 5^{6} \cdot 11 \cdot 17^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.014655653$	$1$		$17$	$92160$	$0.612578$	$170953875/12716$	$1.00324$	$2.81379$	$[1, -1, 0, -867, -8959]$	$y^2+xy=x^3-x^2-867x-8959$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(-17, 34), (-20, 1)]$
84150.dv2	84150ec1	84150.dv	84150ec	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{2} \cdot 3^{9} \cdot 5^{6} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.329944942$	$1$		$3$	$276480$	$1.161884$	$170953875/12716$	$1.00324$	$3.39505$	$[1, -1, 1, -7805, 249697]$	$y^2+xy+y=x^3-x^2-7805x+249697$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(35, 118)]$
107712.bw2	107712ct1	107712.bw	107712ct	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{20} \cdot 3^{9} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$368640$	$1.396887$	$170953875/12716$	$1.00324$	$3.56609$	$[0, 0, 0, -19980, -1014768]$	$y^2=x^3-19980x-1014768$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
107712.bz2	107712db1	107712.bz	107712db	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{20} \cdot 3^{3} \cdot 11 \cdot 17^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.430770450$	$1$		$13$	$122880$	$0.847580$	$170953875/12716$	$1.00324$	$2.99722$	$[0, 0, 0, -2220, 37584]$	$y^2=x^3-2220x+37584$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(10, 128), (-20, 272)]$
107712.db2	107712f1	107712.db	107712f	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{20} \cdot 3^{3} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$122880$	$0.847580$	$170953875/12716$	$1.00324$	$2.99722$	$[0, 0, 0, -2220, -37584]$	$y^2=x^3-2220x-37584$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
107712.dc2	107712l1	107712.dc	107712l	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{20} \cdot 3^{9} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$368640$	$1.396887$	$170953875/12716$	$1.00324$	$3.56609$	$[0, 0, 0, -19980, 1014768]$	$y^2=x^3-19980x+1014768$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
164934.x2	164934ed1	164934.x	164934ed	$2$	$2$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \cdot 17 $	$ 2^{2} \cdot 3^{9} \cdot 7^{6} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.396093617$	$1$		$3$	$552960$	$1.330120$	$170953875/12716$	$1.00324$	$3.37292$	$[1, -1, 0, -15297, -675991]$	$y^2+xy=x^3-x^2-15297x-675991$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(-74, 253)]$
164934.db2	164934ch1	164934.db	164934ch	$2$	$2$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \cdot 17 $	$ 2^{2} \cdot 3^{3} \cdot 7^{6} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$184320$	$0.780814$	$170953875/12716$	$1.00324$	$2.82422$	$[1, -1, 1, -1700, 25603]$	$y^2+xy+y=x^3-x^2-1700x+25603$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
296208.dr2	296208dr1	296208.dr	296208dr	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{14} \cdot 3^{3} \cdot 11^{7} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$3.171436960$	$1$		$3$	$1843200$	$1.699953$	$170953875/12716$	$1.00324$	$3.56842$	$[0, 0, 0, -67155, -6253038]$	$y^2=x^3-67155x-6253038$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(-162, 612)]$
296208.dt2	296208dt1	296208.dt	296208dt	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{14} \cdot 3^{9} \cdot 11^{7} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$5529600$	$2.249260$	$170953875/12716$	$1.00324$	$4.09162$	$[0, 0, 0, -604395, 168832026]$	$y^2=x^3-604395x+168832026$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
457776.dp2	457776dp1	457776.dp	457776dp	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{14} \cdot 3^{9} \cdot 11 \cdot 17^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$4$	$2$	$1$	$13271040$	$2.466919$	$170953875/12716$	$1.00324$	$4.15536$	$[0, 0, 0, -1443555, -623194398]$	$y^2=x^3-1443555x-623194398$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[ ]$
457776.dq2	457776dq1	457776.dq	457776dq	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{14} \cdot 3^{3} \cdot 11 \cdot 17^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$4.196825544$	$1$		$1$	$4423680$	$1.917612$	$170953875/12716$	$1.00324$	$3.64963$	$[0, 0, 0, -160395, 23081274]$	$y^2=x^3-160395x+23081274$	2.3.0.a.1, 66.6.0.a.1, 408.6.0.?, 1496.6.0.?, 4488.12.0.?	$[(1615/3, 7514/3)]$

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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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