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 (22 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
20328.y2	20328u1	20328.y	20328u	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 7 \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$21.89017804$	$1$		$1$	$42240$	$1.313702$	$8788/21$	$0.88390$	$3.90478$	$[0, 1, 0, 5768, -296320]$	$y^2=x^3+x^2+5768x-296320$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(2236631089/4292, 117500779950255/4292)]$
20328.bc2	20328g1	20328.bc	20328g	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 7 \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$5.015280576$	$1$		$1$	$3840$	$0.114755$	$8788/21$	$0.88390$	$2.45441$	$[0, 1, 0, 48, 240]$	$y^2=x^3+x^2+48x+240$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(-55/4, 435/4)]$
40656.bg2	40656b1	40656.bg	40656b	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 7 \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$2.320906521$	$1$		$5$	$7680$	$0.114755$	$8788/21$	$0.88390$	$2.29410$	$[0, -1, 0, 48, -240]$	$y^2=x^3-x^2+48x-240$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(5, 10)]$
40656.bl2	40656o1	40656.bl	40656o	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 7 \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$4$	$2$	$1$	$84480$	$1.313702$	$8788/21$	$0.88390$	$3.64975$	$[0, -1, 0, 5768, 296320]$	$y^2=x^3-x^2+5768x+296320$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[]$
60984.j2	60984o1	60984.j	60984o	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{7} \cdot 7 \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$		$1$	$337920$	$1.863008$	$8788/21$	$0.88390$	$4.11369$	$[0, 0, 0, 51909, 8052550]$	$y^2=x^3+51909x+8052550$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[]$
60984.q2	60984cb1	60984.q	60984cb	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{7} \cdot 7 \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$		$1$	$30720$	$0.664061$	$8788/21$	$0.88390$	$2.80793$	$[0, 0, 0, 429, -6050]$	$y^2=x^3+429x-6050$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[]$
121968.bb2	121968ba1	121968.bb	121968ba	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{7} \cdot 7 \cdot 11^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$3.090420371$	$1$		$13$	$61440$	$0.664061$	$8788/21$	$0.88390$	$2.64174$	$[0, 0, 0, 429, 6050]$	$y^2=x^3+429x+6050$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(11, 110), (-2, 72)]$
121968.bs2	121968bs1	121968.bs	121968bs	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{7} \cdot 7 \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$7.421987241$	$1$		$1$	$675840$	$1.863008$	$8788/21$	$0.88390$	$3.87022$	$[0, 0, 0, 51909, -8052550]$	$y^2=x^3+51909x-8052550$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(2017/4, 45009/4)]$
142296.i2	142296bb1	142296.i	142296bb	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 7^{7} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$11.59214446$	$1$		$1$	$2027520$	$2.286655$	$8788/21$	$0.88390$	$4.24839$	$[0, -1, 0, 282616, 102203004]$	$y^2=x^3-x^2+282616x+102203004$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(-118199/32, 270270917/32)]$
142296.k2	142296cz1	142296.k	142296cz	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 7^{7} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$		$1$	$184320$	$1.087709$	$8788/21$	$0.88390$	$3.03587$	$[0, -1, 0, 2336, -77636]$	$y^2=x^3-x^2+2336x-77636$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[]$
162624.r2	162624hm1	162624.r	162624hm	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{16} \cdot 3 \cdot 7 \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$8.333179752$	$1$		$1$	$675840$	$1.660276$	$8788/21$	$0.88390$	$3.57469$	$[0, -1, 0, 23071, -2393631]$	$y^2=x^3-x^2+23071x-2393631$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(3805/2, 237239/2)]$
162624.bf2	162624hi1	162624.bf	162624hi	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{16} \cdot 3 \cdot 7 \cdot 11^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$4.820515730$	$1$		$7$	$61440$	$0.461328$	$8788/21$	$0.88390$	$2.37566$	$[0, -1, 0, 191, 1729]$	$y^2=x^3-x^2+191x+1729$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(9, 64), (191, 2640)]$
162624.fl2	162624o1	162624.fl	162624o	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{16} \cdot 3 \cdot 7 \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$4.992311731$	$1$		$1$	$61440$	$0.461328$	$8788/21$	$0.88390$	$2.37566$	$[0, 1, 0, 191, -1729]$	$y^2=x^3+x^2+191x-1729$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(109/2, 1251/2)]$
162624.fs2	162624i1	162624.fs	162624i	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{16} \cdot 3 \cdot 7 \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$4$	$2$	$1$	$675840$	$1.660276$	$8788/21$	$0.88390$	$3.57469$	$[0, 1, 0, 23071, 2393631]$	$y^2=x^3+x^2+23071x+2393631$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[]$
284592.gs2	284592gs1	284592.gs	284592gs	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 7^{7} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$6.722449144$	$1$		$3$	$4055040$	$2.286655$	$8788/21$	$0.88390$	$4.01391$	$[0, 1, 0, 282616, -102203004]$	$y^2=x^3+x^2+282616x-102203004$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(16158, 2055060)]$
284592.hd2	284592hd1	284592.hd	284592hd	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 7^{7} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$4.155917956$	$1$		$3$	$368640$	$1.087709$	$8788/21$	$0.88390$	$2.86831$	$[0, 1, 0, 2336, 77636]$	$y^2=x^3+x^2+2336x+77636$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(415, 8526)]$
426888.gd2	426888gd1	426888.gd	426888gd	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{7} \cdot 7^{7} \cdot 11^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$37.74674901$	$1$		$1$	$16220160$	$2.835964$	$8788/21$	$0.88390$	$4.39682$	$[0, 0, 0, 2543541, -2762024650]$	$y^2=x^3+2543541x-2762024650$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(222187193428413073/15145904, 85825629854733578219029305/15145904)]$
426888.gl2	426888gl1	426888.gl	426888gl	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{10} \cdot 3^{7} \cdot 7^{7} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$		$1$	$1474560$	$1.637016$	$8788/21$	$0.88390$	$3.28705$	$[0, 0, 0, 21021, 2075150]$	$y^2=x^3+21021x+2075150$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[]$
487872.mi2	487872mi1	487872.mi	487872mi	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{7} \cdot 7 \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$4$	$2$	$1$	$5406720$	$2.209583$	$8788/21$	$0.88390$	$3.77812$	$[0, 0, 0, 207636, 64420400]$	$y^2=x^3+207636x+64420400$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[]$
487872.mt2	487872mt1	487872.mt	487872mt	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{7} \cdot 7 \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$2.194935021$	$1$		$5$	$491520$	$1.010633$	$8788/21$	$0.88390$	$2.67966$	$[0, 0, 0, 1716, 48400]$	$y^2=x^3+1716x+48400$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(0, 220)]$
487872.nq2	487872nq1	487872.nq	487872nq	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{7} \cdot 7 \cdot 11^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$1$	$1$		$1$	$5406720$	$2.209583$	$8788/21$	$0.88390$	$3.77812$	$[0, 0, 0, 207636, -64420400]$	$y^2=x^3+207636x-64420400$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[]$
487872.ob2	487872ob1	487872.ob	487872ob	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{16} \cdot 3^{7} \cdot 7 \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1848$	$12$	$0$	$6.639749413$	$1$		$1$	$491520$	$1.010633$	$8788/21$	$0.88390$	$2.67966$	$[0, 0, 0, 1716, -48400]$	$y^2=x^3+1716x-48400$	2.3.0.a.1, 88.6.0.?, 168.6.0.?, 462.6.0.?, 1848.12.0.?	$[(1873/4, 84825/4)]$

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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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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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