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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.b1	3192c3	3192.b	3192c	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{4} \cdot 7^{3} \cdot 19^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$1$	$1$		$3$	$24576$	$1.814154$	$22501000029889239268/3620708343$	$[0, -1, 0, -592824, 175883580]$	$y^2=x^3-x^2-592824x+175883580$
6384.v1	6384n3	6384.v	6384n	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{4} \cdot 7^{3} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$2.209406959$	$1$		$3$	$49152$	$1.814154$	$22501000029889239268/3620708343$	$[0, 1, 0, -592824, -175883580]$	$y^2=x^3+x^2-592824x-175883580$
9576.t1	9576v3	9576.t	9576v	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{10} \cdot 7^{3} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$196608$	$2.363461$	$22501000029889239268/3620708343$	$[0, 0, 0, -5335419, -4743521242]$	$y^2=x^3-5335419x-4743521242$
19152.bq1	19152u3	19152.bq	19152u	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{10} \cdot 7^{3} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1.438827442$	$1$		$7$	$393216$	$2.363461$	$22501000029889239268/3620708343$	$[0, 0, 0, -5335419, 4743521242]$	$y^2=x^3-5335419x+4743521242$
22344.bb1	22344t4	22344.bb	22344t	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{4} \cdot 7^{9} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$13.46734830$	$1$		$1$	$1179648$	$2.787109$	$22501000029889239268/3620708343$	$[0, 1, 0, -29048392, -60269971168]$	$y^2=x^3+x^2-29048392x-60269971168$
25536.bk1	25536cm4	25536.bk	25536cm	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{16} \cdot 3^{4} \cdot 7^{3} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$1$	$1$		$1$	$393216$	$2.160728$	$22501000029889239268/3620708343$	$[0, -1, 0, -2371297, -1404697343]$	$y^2=x^3-x^2-2371297x-1404697343$
25536.dh1	25536bb4	25536.dh	25536bb	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{16} \cdot 3^{4} \cdot 7^{3} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$1$	$1$		$1$	$393216$	$2.160728$	$22501000029889239268/3620708343$	$[0, 1, 0, -2371297, 1404697343]$	$y^2=x^3+x^2-2371297x+1404697343$
44688.bm1	44688m4	44688.bm	44688m	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{4} \cdot 7^{9} \cdot 19^{4} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$6.920372498$	$1$		$3$	$2359296$	$2.787109$	$22501000029889239268/3620708343$	$[0, -1, 0, -29048392, 60269971168]$	$y^2=x^3-x^2-29048392x+60269971168$
60648.w1	60648bk4	60648.w	60648bk	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{4} \cdot 7^{3} \cdot 19^{10} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$31.92223628$	$1$		$7$	$8847360$	$3.286373$	$22501000029889239268/3620708343$	$[0, 1, 0, -214009584, -1205101417968]$	$y^2=x^3+x^2-214009584x-1205101417968$
67032.v1	67032ch4	67032.v	67032ch	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{10} \cdot 7^{9} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$9437184$	$3.336414$	$22501000029889239268/3620708343$	$[0, 0, 0, -261435531, 1627027786006]$	$y^2=x^3-261435531x+1627027786006$
76608.t1	76608bk4	76608.t	76608bk	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{16} \cdot 3^{10} \cdot 7^{3} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$3145728$	$2.710033$	$22501000029889239268/3620708343$	$[0, 0, 0, -21341676, -37948169936]$	$y^2=x^3-21341676x-37948169936$
76608.bw1	76608fu4	76608.bw	76608fu	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{16} \cdot 3^{10} \cdot 7^{3} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$0.999080123$	$1$		$5$	$3145728$	$2.710033$	$22501000029889239268/3620708343$	$[0, 0, 0, -21341676, 37948169936]$	$y^2=x^3-21341676x+37948169936$
79800.bm1	79800bu4	79800.bm	79800bu	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{4} \cdot 5^{6} \cdot 7^{3} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$0.615713594$	$1$		$9$	$3145728$	$2.618874$	$22501000029889239268/3620708343$	$[0, 1, 0, -14820608, 21955806288]$	$y^2=x^3+x^2-14820608x+21955806288$
121296.n1	121296v4	121296.n	121296v	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{4} \cdot 7^{3} \cdot 19^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$2.924006815$	$1$		$3$	$17694720$	$3.286373$	$22501000029889239268/3620708343$	$[0, -1, 0, -214009584, 1205101417968]$	$y^2=x^3-x^2-214009584x+1205101417968$
134064.z1	134064ds4	134064.z	134064ds	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{10} \cdot 7^{9} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$18874368$	$3.336414$	$22501000029889239268/3620708343$	$[0, 0, 0, -261435531, -1627027786006]$	$y^2=x^3-261435531x-1627027786006$
159600.bo1	159600gy4	159600.bo	159600gy	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{4} \cdot 5^{6} \cdot 7^{3} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$19.00312667$	$1$		$1$	$6291456$	$2.618874$	$22501000029889239268/3620708343$	$[0, -1, 0, -14820608, -21955806288]$	$y^2=x^3-x^2-14820608x-21955806288$
178752.bk1	178752ir4	178752.bk	178752ir	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{16} \cdot 3^{4} \cdot 7^{9} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$8.418344716$	$1$		$1$	$18874368$	$3.133682$	$22501000029889239268/3620708343$	$[0, -1, 0, -116193569, -482043575775]$	$y^2=x^3-x^2-116193569x-482043575775$
178752.gf1	178752o3	178752.gf	178752o	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{16} \cdot 3^{4} \cdot 7^{9} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$1$	$1$		$1$	$18874368$	$3.133682$	$22501000029889239268/3620708343$	$[0, 1, 0, -116193569, 482043575775]$	$y^2=x^3+x^2-116193569x+482043575775$
181944.bv1	181944ce3	181944.bv	181944ce	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{10} \cdot 7^{3} \cdot 19^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$14.22833173$	$1$		$1$	$70778880$	$3.835678$	$22501000029889239268/3620708343$	$[0, 0, 0, -1926086259, 32535812198878]$	$y^2=x^3-1926086259x+32535812198878$
239400.ef1	239400ef4	239400.ef	239400ef	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{10} \cdot 5^{6} \cdot 7^{3} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$25165824$	$3.168179$	$22501000029889239268/3620708343$	$[0, 0, 0, -133385475, -592940155250]$	$y^2=x^3-133385475x-592940155250$
363888.ea1	363888ea4	363888.ea	363888ea	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{10} \cdot 7^{3} \cdot 19^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$141557760$	$3.835678$	$22501000029889239268/3620708343$	$[0, 0, 0, -1926086259, -32535812198878]$	$y^2=x^3-1926086259x-32535812198878$
386232.j1	386232j4	386232.j	386232j	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 $	$ 2^{10} \cdot 3^{4} \cdot 7^{3} \cdot 11^{6} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$31457280$	$3.013103$	$22501000029889239268/3620708343$	$[0, -1, 0, -71731744, -233814118052]$	$y^2=x^3-x^2-71731744x-233814118052$
424536.bm1	424536bm3	424536.bm	424536bm	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} $	$ 2^{10} \cdot 3^{4} \cdot 7^{9} \cdot 19^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.14	2B	$1$	$9$	$3$	$1$	$424673280$	$4.259331$	$22501000029889239268/3620708343$	$[0, -1, 0, -10486469632, 413328813423772]$	$y^2=x^3-x^2-10486469632x+413328813423772$
478800.ba1	478800ba3	478800.ba	478800ba	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{10} \cdot 5^{6} \cdot 7^{3} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$50331648$	$3.168179$	$22501000029889239268/3620708343$	$[0, 0, 0, -133385475, 592940155250]$	$y^2=x^3-133385475x+592940155250$
485184.do1	485184do4	485184.do	485184do	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{16} \cdot 3^{4} \cdot 7^{3} \cdot 19^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$1$	$1$		$1$	$141557760$	$3.632946$	$22501000029889239268/3620708343$	$[0, -1, 0, -856038337, -9639955305407]$	$y^2=x^3-x^2-856038337x-9639955305407$
485184.ij1	485184ij3	485184.ij	485184ij	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{16} \cdot 3^{4} \cdot 7^{3} \cdot 19^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$4.905093081$	$1$		$3$	$141557760$	$3.632946$	$22501000029889239268/3620708343$	$[0, 1, 0, -856038337, 9639955305407]$	$y^2=x^3+x^2-856038337x+9639955305407$

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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.