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Conductor	j-invariant	Rank	Torsion	Complex multiplication

Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image

Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $\|Ш\|	Nonmax$\ \ell$

Curves per isogeny class	Reduction	Integral points	Faltings height

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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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
3192.b4	3192c1	3192.b	3192c	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{4} \cdot 3^{16} \cdot 7^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1$	$1$		$1$	$6144$	$1.121006$	$572616640141312/280535480757$	$[0, -1, 0, -4359, -41940]$	$y^2=x^3-x^2-4359x-41940$
6384.v4	6384n1	6384.v	6384n	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{4} \cdot 3^{16} \cdot 7^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$0.552351739$	$1$		$5$	$12288$	$1.121006$	$572616640141312/280535480757$	$[0, 1, 0, -4359, 41940]$	$y^2=x^3+x^2-4359x+41940$
9576.t4	9576v1	9576.t	9576v	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{4} \cdot 3^{22} \cdot 7^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$49152$	$1.670313$	$572616640141312/280535480757$	$[0, 0, 0, -39234, 1171613]$	$y^2=x^3-39234x+1171613$
19152.bq4	19152u1	19152.bq	19152u	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{4} \cdot 3^{22} \cdot 7^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$5.755309768$	$1$		$3$	$98304$	$1.670313$	$572616640141312/280535480757$	$[0, 0, 0, -39234, -1171613]$	$y^2=x^3-39234x-1171613$
22344.bb4	22344t1	22344.bb	22344t	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{4} \cdot 3^{16} \cdot 7^{9} \cdot 19 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$3.366837075$	$1$		$5$	$294912$	$2.093964$	$572616640141312/280535480757$	$[0, 1, 0, -213607, 14812622]$	$y^2=x^3+x^2-213607x+14812622$
25536.bk4	25536cm1	25536.bk	25536cm	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{16} \cdot 7^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$1$	$1$		$1$	$98304$	$1.467581$	$572616640141312/280535480757$	$[0, -1, 0, -17437, 352957]$	$y^2=x^3-x^2-17437x+352957$
25536.dh4	25536bb1	25536.dh	25536bb	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{16} \cdot 7^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$1$	$1$		$1$	$98304$	$1.467581$	$572616640141312/280535480757$	$[0, 1, 0, -17437, -352957]$	$y^2=x^3+x^2-17437x-352957$
44688.bm4	44688m1	44688.bm	44688m	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{4} \cdot 3^{16} \cdot 7^{9} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$27.68148999$	$1$		$1$	$589824$	$2.093964$	$572616640141312/280535480757$	$[0, -1, 0, -213607, -14812622]$	$y^2=x^3-x^2-213607x-14812622$
60648.w4	60648bk1	60648.w	60648bk	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{4} \cdot 3^{16} \cdot 7^{3} \cdot 19^{7} $	$2$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$7.980559072$	$1$		$19$	$2211840$	$2.593227$	$572616640141312/280535480757$	$[0, 1, 0, -1573719, 297108522]$	$y^2=x^3+x^2-1573719x+297108522$
67032.v4	67032ch1	67032.v	67032ch	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ 2^{4} \cdot 3^{22} \cdot 7^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$2359296$	$2.643269$	$572616640141312/280535480757$	$[0, 0, 0, -1922466, -401863259]$	$y^2=x^3-1922466x-401863259$
76608.t4	76608bk1	76608.t	76608bk	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{22} \cdot 7^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$786432$	$2.016888$	$572616640141312/280535480757$	$[0, 0, 0, -156936, 9372904]$	$y^2=x^3-156936x+9372904$
76608.bw4	76608fu1	76608.bw	76608fu	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{22} \cdot 7^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3.996320495$	$1$		$3$	$786432$	$2.016888$	$572616640141312/280535480757$	$[0, 0, 0, -156936, -9372904]$	$y^2=x^3-156936x-9372904$
79800.bm4	79800bu1	79800.bm	79800bu	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{4} \cdot 3^{16} \cdot 5^{6} \cdot 7^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$0.615713594$	$1$		$9$	$786432$	$1.925726$	$572616640141312/280535480757$	$[0, 1, 0, -108983, -5460462]$	$y^2=x^3+x^2-108983x-5460462$
121296.n4	121296v1	121296.n	121296v	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{4} \cdot 3^{16} \cdot 7^{3} \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$11.69602726$	$1$		$1$	$4423680$	$2.593227$	$572616640141312/280535480757$	$[0, -1, 0, -1573719, -297108522]$	$y^2=x^3-x^2-1573719x-297108522$
134064.z4	134064ds1	134064.z	134064ds	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ 2^{4} \cdot 3^{22} \cdot 7^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$4718592$	$2.643269$	$572616640141312/280535480757$	$[0, 0, 0, -1922466, 401863259]$	$y^2=x^3-1922466x+401863259$
159600.bo4	159600gy1	159600.bo	159600gy	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{4} \cdot 3^{16} \cdot 5^{6} \cdot 7^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$19.00312667$	$1$		$1$	$1572864$	$1.925726$	$572616640141312/280535480757$	$[0, -1, 0, -108983, 5460462]$	$y^2=x^3-x^2-108983x+5460462$
178752.bk4	178752ir1	178752.bk	178752ir	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{16} \cdot 7^{9} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$8.418344716$	$1$		$3$	$4718592$	$2.440536$	$572616640141312/280535480757$	$[0, -1, 0, -854429, 119355405]$	$y^2=x^3-x^2-854429x+119355405$
178752.gf4	178752o1	178752.gf	178752o	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{16} \cdot 7^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$1$	$1$		$1$	$4718592$	$2.440536$	$572616640141312/280535480757$	$[0, 1, 0, -854429, -119355405]$	$y^2=x^3+x^2-854429x-119355405$
181944.bv4	181944ce1	181944.bv	181944ce	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ 2^{4} \cdot 3^{22} \cdot 7^{3} \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$14.22833173$	$1$		$1$	$17694720$	$3.142532$	$572616640141312/280535480757$	$[0, 0, 0, -14163474, -8036093567]$	$y^2=x^3-14163474x-8036093567$
239400.ef4	239400ef1	239400.ef	239400ef	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{4} \cdot 3^{22} \cdot 5^{6} \cdot 7^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$6291456$	$2.475033$	$572616640141312/280535480757$	$[0, 0, 0, -980850, 146451625]$	$y^2=x^3-980850x+146451625$
363888.ea4	363888ea1	363888.ea	363888ea	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ 2^{4} \cdot 3^{22} \cdot 7^{3} \cdot 19^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$35389440$	$3.142532$	$572616640141312/280535480757$	$[0, 0, 0, -14163474, 8036093567]$	$y^2=x^3-14163474x+8036093567$
386232.j4	386232j1	386232.j	386232j	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 $	$ 2^{4} \cdot 3^{16} \cdot 7^{3} \cdot 11^{6} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$7864320$	$2.319954$	$572616640141312/280535480757$	$[0, -1, 0, -527479, 57932008]$	$y^2=x^3-x^2-527479x+57932008$
424536.bm4	424536bm1	424536.bm	424536bm	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} $	$ 2^{4} \cdot 3^{16} \cdot 7^{9} \cdot 19^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.14	2B	$1$	$9$	$3$	$1$	$106168320$	$3.566181$	$572616640141312/280535480757$	$[0, -1, 0, -77112247, -102062447528]$	$y^2=x^3-x^2-77112247x-102062447528$
478800.ba4	478800ba1	478800.ba	478800ba	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{4} \cdot 3^{22} \cdot 5^{6} \cdot 7^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$12582912$	$2.475033$	$572616640141312/280535480757$	$[0, 0, 0, -980850, -146451625]$	$y^2=x^3-980850x-146451625$
485184.do4	485184do1	485184.do	485184do	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{16} \cdot 7^{3} \cdot 19^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$1$	$1$		$1$	$35389440$	$2.939800$	$572616640141312/280535480757$	$[0, -1, 0, -6294877, 2383163053]$	$y^2=x^3-x^2-6294877x+2383163053$
485184.ij4	485184ij1	485184.ij	485184ij	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{16} \cdot 7^{3} \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$1.226273270$	$1$		$3$	$35389440$	$2.939800$	$572616640141312/280535480757$	$[0, 1, 0, -6294877, -2383163053]$	$y^2=x^3+x^2-6294877x-2383163053$

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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.