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 (26 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
3192.k2	3192o2	3192.k	3192o	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19 $	$ - 2^{8} \cdot 3^{3} \cdot 7^{2} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$0.270098968$	$1$		$11$	$1536$	$0.238290$	$427694384/477603$	$0.84983$	$3.15045$	$[0, 1, 0, 100, -336]$	$y^2=x^3+x^2+100x-336$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(10, 42)]$
6384.b2	6384f2	6384.b	6384f	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19 $	$ - 2^{8} \cdot 3^{3} \cdot 7^{2} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$0.968442311$	$1$		$5$	$3072$	$0.238290$	$427694384/477603$	$0.84983$	$2.90121$	$[0, -1, 0, 100, 336]$	$y^2=x^3-x^2+100x+336$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(4, 28)]$
9576.y2	9576h2	9576.y	9576h	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 $	$ - 2^{8} \cdot 3^{9} \cdot 7^{2} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$12288$	$0.787596$	$427694384/477603$	$0.84983$	$3.49195$	$[0, 0, 0, 897, 9970]$	$y^2=x^3+897x+9970$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
19152.cb2	19152bb2	19152.cb	19152bb	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 $	$ - 2^{8} \cdot 3^{9} \cdot 7^{2} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$24576$	$0.787596$	$427694384/477603$	$0.84983$	$3.24647$	$[0, 0, 0, 897, -9970]$	$y^2=x^3+897x-9970$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
22344.p2	22344bb2	22344.p	22344bb	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{8} \cdot 3^{3} \cdot 7^{8} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$73728$	$1.211245$	$427694384/477603$	$0.84983$	$3.70415$	$[0, -1, 0, 4884, 125028]$	$y^2=x^3-x^2+4884x+125028$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
25536.bs2	25536j2	25536.bs	25536j	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ - 2^{14} \cdot 3^{3} \cdot 7^{2} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$24576$	$0.584864$	$427694384/477603$	$0.84983$	$2.91471$	$[0, -1, 0, 399, -3087]$	$y^2=x^3-x^2+399x-3087$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
25536.dq2	25536di2	25536.dq	25536di	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ - 2^{14} \cdot 3^{3} \cdot 7^{2} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$24576$	$0.584864$	$427694384/477603$	$0.84983$	$2.91471$	$[0, 1, 0, 399, 3087]$	$y^2=x^3+x^2+399x+3087$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
44688.ds2	44688bf2	44688.ds	44688bf	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{8} \cdot 3^{3} \cdot 7^{8} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$2.102019284$	$1$		$3$	$147456$	$1.211245$	$427694384/477603$	$0.84983$	$3.46437$	$[0, 1, 0, 4884, -125028]$	$y^2=x^3+x^2+4884x-125028$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(198, 2940)]$
60648.b2	60648h2	60648.b	60648h	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 7^{2} \cdot 19^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$552960$	$1.710508$	$427694384/477603$	$0.84983$	$3.91232$	$[0, -1, 0, 35980, 2520756]$	$y^2=x^3-x^2+35980x+2520756$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
67032.b2	67032bh2	67032.b	67032bh	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ - 2^{8} \cdot 3^{9} \cdot 7^{8} \cdot 19^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$2.199058586$	$1$		$17$	$589824$	$1.760551$	$427694384/477603$	$0.84983$	$3.93112$	$[0, 0, 0, 43953, -3419710]$	$y^2=x^3+43953x-3419710$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(127, 2052), (203, 3724)]$
76608.g2	76608by2	76608.g	76608by	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ - 2^{14} \cdot 3^{9} \cdot 7^{2} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.132613760$	$1$		$7$	$196608$	$1.134169$	$427694384/477603$	$0.84983$	$3.21609$	$[0, 0, 0, 3588, 79760]$	$y^2=x^3+3588x+79760$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(37, 513)]$
76608.j2	76608fe2	76608.j	76608fe	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ - 2^{14} \cdot 3^{9} \cdot 7^{2} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$196608$	$1.134169$	$427694384/477603$	$0.84983$	$3.21609$	$[0, 0, 0, 3588, -79760]$	$y^2=x^3+3588x-79760$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
79800.y2	79800c2	79800.y	79800c	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{6} \cdot 7^{2} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$122880$	$1.043009$	$427694384/477603$	$0.84983$	$3.10754$	$[0, -1, 0, 2492, -46988]$	$y^2=x^3-x^2+2492x-46988$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
121296.bu2	121296bp2	121296.bu	121296bp	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 7^{2} \cdot 19^{8} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$3.955839017$	$1$		$11$	$1105920$	$1.710508$	$427694384/477603$	$0.84983$	$3.68066$	$[0, 1, 0, 35980, -2520756]$	$y^2=x^3+x^2+35980x-2520756$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(595, 15162), (234, 4332)]$
134064.h2	134064di2	134064.h	134064di	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ - 2^{8} \cdot 3^{9} \cdot 7^{8} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.812441521$	$1$		$5$	$1179648$	$1.760551$	$427694384/477603$	$0.84983$	$3.70032$	$[0, 0, 0, 43953, 3419710]$	$y^2=x^3+43953x+3419710$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(-7, 1764)]$
159600.dr2	159600fu2	159600.dr	159600fu	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{6} \cdot 7^{2} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.238816945$	$1$		$5$	$245760$	$1.043009$	$427694384/477603$	$0.84983$	$2.92775$	$[0, 1, 0, 2492, 46988]$	$y^2=x^3+x^2+2492x+46988$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(2, 228)]$
178752.e2	178752cy2	178752.e	178752cy	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{14} \cdot 3^{3} \cdot 7^{8} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$1179648$	$1.557817$	$427694384/477603$	$0.84983$	$3.41114$	$[0, -1, 0, 19535, -1019759]$	$y^2=x^3-x^2+19535x-1019759$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
178752.fj2	178752fr2	178752.fj	178752fr	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{14} \cdot 3^{3} \cdot 7^{8} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.506581794$	$1$		$5$	$1179648$	$1.557817$	$427694384/477603$	$0.84983$	$3.41114$	$[0, 1, 0, 19535, 1019759]$	$y^2=x^3+x^2+19535x+1019759$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(2, 1029)]$
181944.cl2	181944w2	181944.cl	181944w	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ - 2^{8} \cdot 3^{9} \cdot 7^{2} \cdot 19^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$4423680$	$2.259815$	$427694384/477603$	$0.84983$	$4.10169$	$[0, 0, 0, 323817, -68384230]$	$y^2=x^3+323817x-68384230$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
239400.cp2	239400cp2	239400.cp	239400cp	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{6} \cdot 7^{2} \cdot 19^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.352507885$	$1$		$27$	$983040$	$1.592316$	$427694384/477603$	$0.84983$	$3.36410$	$[0, 0, 0, 22425, 1246250]$	$y^2=x^3+22425x+1246250$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(25, 1350), (-29, 756)]$
363888.fk2	363888fk2	363888.fk	363888fk	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ - 2^{8} \cdot 3^{9} \cdot 7^{2} \cdot 19^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$4$	$2$	$1$	$8847360$	$2.259815$	$427694384/477603$	$0.84983$	$3.87965$	$[0, 0, 0, 323817, 68384230]$	$y^2=x^3+323817x+68384230$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
386232.bg2	386232bg2	386232.bg	386232bg	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 $	$ - 2^{8} \cdot 3^{3} \cdot 7^{2} \cdot 11^{6} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.374324178$	$1$		$7$	$1966080$	$1.437237$	$427694384/477603$	$0.84983$	$3.09436$	$[0, 1, 0, 12060, 495504]$	$y^2=x^3+x^2+12060x+495504$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(84, 1452)]$
424536.ej2	424536ej2	424536.ej	424536ej	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 7^{8} \cdot 19^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$4$	$2$	$1$	$26542080$	$2.683464$	$427694384/477603$	$0.84983$	$4.22581$	$[0, 1, 0, 1763004, -868145328]$	$y^2=x^3+x^2+1763004x-868145328$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
478800.gp2	478800gp2	478800.gp	478800gp	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{6} \cdot 7^{2} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$4.153522514$	$1$		$3$	$1966080$	$1.592316$	$427694384/477603$	$0.84983$	$3.18582$	$[0, 0, 0, 22425, -1246250]$	$y^2=x^3+22425x-1246250$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(1589, 63612)]$
485184.es2	485184es2	485184.es	485184es	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ - 2^{14} \cdot 3^{3} \cdot 7^{2} \cdot 19^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$9$	$3$	$1$	$8847360$	$2.057083$	$427694384/477603$	$0.84983$	$3.60858$	$[0, -1, 0, 143919, -20309967]$	$y^2=x^3-x^2+143919x-20309967$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[]$
485184.jf2	485184jf2	485184.jf	485184jf	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ - 2^{14} \cdot 3^{3} \cdot 7^{2} \cdot 19^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$5.915002368$	$1$		$1$	$8847360$	$2.057083$	$427694384/477603$	$0.84983$	$3.60858$	$[0, 1, 0, 143919, 20309967]$	$y^2=x^3+x^2+143919x+20309967$	2.3.0.a.1, 6.6.0.a.1, 532.6.0.?, 1596.12.0.?	$[(30981/10, 9732921/10)]$

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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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