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 (28 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
4056.k1	4056j2	4056.k	4056j	$2$	$2$	$ 2^{3} \cdot 3 \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$0.469874516$	$1$		$9$	$4608$	$0.712502$	$34909201168/81$	$1.02428$	$4.51568$	$[0, 1, 0, -5620, 160304]$	$y^2=x^3+x^2-5620x+160304$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(44, 12)]$
4056.r1	4056s2	4056.r	4056s	$2$	$2$	$ 2^{3} \cdot 3 \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1$	$1$		$1$	$59904$	$1.994976$	$34909201168/81$	$1.02428$	$6.36808$	$[0, 1, 0, -949836, 355987152]$	$y^2=x^3+x^2-949836x+355987152$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
8112.a1	8112i2	8112.a	8112i	$2$	$2$	$ 2^{4} \cdot 3 \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1$	$1$		$1$	$9216$	$0.712502$	$34909201168/81$	$1.02428$	$4.16794$	$[0, -1, 0, -5620, -160304]$	$y^2=x^3-x^2-5620x-160304$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
8112.p1	8112h2	8112.p	8112h	$2$	$2$	$ 2^{4} \cdot 3 \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1$	$9$	$3$	$1$	$119808$	$1.994976$	$34909201168/81$	$1.02428$	$5.87770$	$[0, -1, 0, -949836, -355987152]$	$y^2=x^3-x^2-949836x-355987152$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
12168.a1	12168k2	12168.a	12168k	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{10} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$10.51773674$	$1$		$1$	$479232$	$2.544281$	$34909201168/81$	$1.02428$	$6.32509$	$[0, 0, 0, -8548527, -9620201630]$	$y^2=x^3-8548527x-9620201630$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(179591/5, 68428764/5)]$
12168.w1	12168x2	12168.w	12168x	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{10} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1$	$1$		$1$	$36864$	$1.261808$	$34909201168/81$	$1.02428$	$4.68904$	$[0, 0, 0, -50583, -4378790]$	$y^2=x^3-50583x-4378790$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
24336.b1	24336x2	24336.b	24336x	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{10} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$2.181918114$	$1$		$5$	$958464$	$2.544281$	$34909201168/81$	$1.02428$	$5.89100$	$[0, 0, 0, -8548527, 9620201630]$	$y^2=x^3-8548527x+9620201630$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(1693, 324)]$
24336.cg1	24336w2	24336.cg	24336w	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{10} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1.919344534$	$1$		$3$	$73728$	$1.261808$	$34909201168/81$	$1.02428$	$4.36723$	$[0, 0, 0, -50583, 4378790]$	$y^2=x^3-50583x+4378790$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(205, 1620)]$
32448.b1	32448v2	32448.b	32448v	$2$	$2$	$ 2^{6} \cdot 3 \cdot 13^{2} $	$ 2^{14} \cdot 3^{4} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1$	$1$		$1$	$958464$	$2.341549$	$34909201168/81$	$1.02428$	$5.49364$	$[0, -1, 0, -3799345, 2851696561]$	$y^2=x^3-x^2-3799345x+2851696561$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
32448.bt1	32448u2	32448.bt	32448u	$2$	$2$	$ 2^{6} \cdot 3 \cdot 13^{2} $	$ 2^{14} \cdot 3^{4} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1$	$1$		$1$	$73728$	$1.059074$	$34909201168/81$	$1.02428$	$4.01207$	$[0, -1, 0, -22481, 1304913]$	$y^2=x^3-x^2-22481x+1304913$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
32448.bx1	32448dp2	32448.bx	32448dp	$2$	$2$	$ 2^{6} \cdot 3 \cdot 13^{2} $	$ 2^{14} \cdot 3^{4} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1$	$4$	$2$	$1$	$958464$	$2.341549$	$34909201168/81$	$1.02428$	$5.49364$	$[0, 1, 0, -3799345, -2851696561]$	$y^2=x^3+x^2-3799345x-2851696561$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
32448.do1	32448do2	32448.do	32448do	$2$	$2$	$ 2^{6} \cdot 3 \cdot 13^{2} $	$ 2^{14} \cdot 3^{4} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1$	$4$	$2$	$1$	$73728$	$1.059074$	$34909201168/81$	$1.02428$	$4.01207$	$[0, 1, 0, -22481, -1304913]$	$y^2=x^3+x^2-22481x-1304913$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
97344.c1	97344dp2	97344.c	97344dp	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 13^{2} $	$ 2^{14} \cdot 3^{10} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$4.747849594$	$1$		$3$	$589824$	$1.608381$	$34909201168/81$	$1.02428$	$4.20221$	$[0, 0, 0, -202332, -35030320]$	$y^2=x^3-202332x-35030320$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(572, 6032)]$
97344.h1	97344gs2	97344.h	97344gs	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 13^{2} $	$ 2^{14} \cdot 3^{10} \cdot 13^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$3.202987711$	$1$		$13$	$589824$	$1.608381$	$34909201168/81$	$1.02428$	$4.20221$	$[0, 0, 0, -202332, 35030320]$	$y^2=x^3-202332x+35030320$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(248, 324), (269, 261)]$
97344.gl1	97344gq2	97344.gl	97344gq	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 13^{2} $	$ 2^{14} \cdot 3^{10} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$1$	$4$	$2$	$1$	$7667712$	$2.890858$	$34909201168/81$	$1.02428$	$5.54207$	$[0, 0, 0, -34194108, 76961613040]$	$y^2=x^3-34194108x+76961613040$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
97344.go1	97344do2	97344.go	97344do	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 13^{2} $	$ 2^{14} \cdot 3^{10} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$624$	$192$	$5$	$40.22266748$	$1$		$1$	$7667712$	$2.890858$	$34909201168/81$	$1.02428$	$5.54207$	$[0, 0, 0, -34194108, -76961613040]$	$y^2=x^3-34194108x-76961613040$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(-10597721655868792631/56013530, 62596022880935039112463653/56013530)]$
101400.l1	101400o2	101400.l	101400o	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 5^{6} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$3120$	$192$	$5$	$1$	$1$		$1$	$4792320$	$2.799694$	$34909201168/81$	$1.02428$	$5.42754$	$[0, -1, 0, -23745908, 44545885812]$	$y^2=x^3-x^2-23745908x+44545885812$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
101400.bm1	101400ci2	101400.bm	101400ci	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 5^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$3120$	$192$	$5$	$1.082288786$	$1$		$7$	$368640$	$1.517221$	$34909201168/81$	$1.02428$	$4.09242$	$[0, -1, 0, -140508, 20319012]$	$y^2=x^3-x^2-140508x+20319012$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(216, 18)]$
198744.a1	198744bh2	198744.a	198744bh	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 7^{6} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$4368$	$192$	$5$	$1$	$1$		$1$	$21565440$	$2.967930$	$34909201168/81$	$1.02428$	$5.29364$	$[0, -1, 0, -46541980, -122196677084]$	$y^2=x^3-x^2-46541980x-122196677084$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
198744.br1	198744dz2	198744.br	198744dz	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 7^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$4368$	$192$	$5$	$10.54975111$	$1$		$1$	$1658880$	$1.685457$	$34909201168/81$	$1.02428$	$4.03217$	$[0, -1, 0, -275396, -55535052]$	$y^2=x^3-x^2-275396x-55535052$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(-915734/55, 1719236/55)]$
202800.gp1	202800hp2	202800.gp	202800hp	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 5^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$3120$	$192$	$5$	$3.454055233$	$1$		$3$	$737280$	$1.517221$	$34909201168/81$	$1.02428$	$3.86029$	$[0, 1, 0, -140508, -20319012]$	$y^2=x^3+x^2-140508x-20319012$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(1083, 33150)]$
202800.jf1	202800ii2	202800.jf	202800ii	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 5^{6} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$3120$	$192$	$5$	$18.84925570$	$1$		$1$	$9584640$	$2.799694$	$34909201168/81$	$1.02428$	$5.11968$	$[0, 1, 0, -23745908, -44545885812]$	$y^2=x^3+x^2-23745908x-44545885812$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(-4203169619/1222, 520587771573/1222)]$
304200.bu1	304200bu2	304200.bu	304200bu	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{10} \cdot 5^{6} \cdot 13^{9} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$3120$	$192$	$5$	$24.17593026$	$1$		$9$	$38338560$	$3.349003$	$34909201168/81$	$1.02428$	$5.47736$	$[0, 0, 0, -213713175, -1202525203750]$	$y^2=x^3-213713175x-1202525203750$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(-8441, 1548), (31225, 4750650)]$
304200.eg1	304200eg2	304200.eg	304200eg	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{10} \cdot 5^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$3120$	$192$	$5$	$7.496874872$	$1$		$1$	$2949120$	$2.066528$	$34909201168/81$	$1.02428$	$4.25841$	$[0, 0, 0, -1264575, -547348750]$	$y^2=x^3-1264575x-547348750$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(26650/3, 3974750/3)]$
397488.fm1	397488fm2	397488.fm	397488fm	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 7^{6} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$4368$	$192$	$5$	$1$	$1$		$1$	$43130880$	$2.967930$	$34909201168/81$	$1.02428$	$5.00904$	$[0, 1, 0, -46541980, 122196677084]$	$y^2=x^3+x^2-46541980x+122196677084$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
397488.ke1	397488ke2	397488.ke	397488ke	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 7^{6} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$4368$	$192$	$5$	$1$	$1$		$1$	$3317760$	$1.685457$	$34909201168/81$	$1.02428$	$3.81539$	$[0, 1, 0, -275396, 55535052]$	$y^2=x^3+x^2-275396x+55535052$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$
490776.bv1	490776bv2	490776.bv	490776bv	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 11^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$6864$	$192$	$5$	$2.162913509$	$1$		$5$	$6451200$	$1.911449$	$34909201168/81$	$1.02428$	$3.96096$	$[0, 1, 0, -680060, -216084816]$	$y^2=x^3+x^2-680060x-216084816$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[(-476, 12)]$
490776.cz1	490776cz2	490776.cz	490776cz	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{4} \cdot 11^{6} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.122	2B	$6864$	$192$	$5$	$1$	$4$	$2$	$1$	$83865600$	$3.193924$	$34909201168/81$	$1.02428$	$5.13541$	$[0, 1, 0, -114930196, -474278620048]$	$y^2=x^3+x^2-114930196x-474278620048$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 26.6.0.b.1, 48.48.1.hj.2, $\ldots$	$[ ]$

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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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 (28 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.

Refine search