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	Nonmax$\ \ell$	Adelic level	Adelic index	Adelic genus

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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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images
3192.h2	3192j2	3192.h	3192j	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{2} \cdot 7^{4} \cdot 19^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.4	2Cs	$456$	$48$	$0$	$1$	$1$		$3$	$2560$	$0.642025$	$93280467172/7800849$	$[0, -1, 0, -952, 10780]$	$y^2=x^3-x^2-952x+10780$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 228.24.0.?, 456.48.0.?
6384.bg2	6384p2	6384.bg	6384p	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{2} \cdot 7^{4} \cdot 19^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.3	2Cs	$456$	$48$	$0$	$1$	$1$		$3$	$5120$	$0.642025$	$93280467172/7800849$	$[0, 1, 0, -952, -10780]$	$y^2=x^3+x^2-952x-10780$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.1, 228.24.0.?, 456.48.0.?
9576.e2	9576g2	9576.e	9576g	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{8} \cdot 7^{4} \cdot 19^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$456$	$48$	$0$	$1$	$1$		$3$	$20480$	$1.191332$	$93280467172/7800849$	$[0, 0, 0, -8571, -282490]$	$y^2=x^3-8571x-282490$	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.2, 76.12.0.?, $\ldots$
19152.h2	19152ba2	19152.h	19152ba	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{8} \cdot 7^{4} \cdot 19^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$456$	$48$	$0$	$1.121371363$	$1$		$37$	$40960$	$1.191332$	$93280467172/7800849$	$[0, 0, 0, -8571, 282490]$	$y^2=x^3-8571x+282490$	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.1, 76.12.0.?, $\ldots$
22344.r2	22344bj2	22344.r	22344bj	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{2} \cdot 7^{10} \cdot 19^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$3192$	$48$	$0$	$8.229049189$	$1$		$3$	$122880$	$1.614981$	$93280467172/7800849$	$[0, 1, 0, -46664, -3604224]$	$y^2=x^3+x^2-46664x-3604224$	2.6.0.a.1, 8.12.0.b.1, 28.12.0-2.a.1.1, 56.24.0-8.b.1.2, 228.12.0.?, $\ldots$
25536.m2	25536ch2	25536.m	25536ch	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{16} \cdot 3^{2} \cdot 7^{4} \cdot 19^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.4	2Cs	$456$	$48$	$0$	$1.592816329$	$1$		$9$	$40960$	$0.988599$	$93280467172/7800849$	$[0, -1, 0, -3809, -82431]$	$y^2=x^3-x^2-3809x-82431$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 228.24.0.?, 456.48.0.?
25536.ce2	25536bj2	25536.ce	25536bj	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ 2^{16} \cdot 3^{2} \cdot 7^{4} \cdot 19^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.3	2Cs	$456$	$48$	$0$	$3.451501679$	$1$		$5$	$40960$	$0.988599$	$93280467172/7800849$	$[0, 1, 0, -3809, 82431]$	$y^2=x^3+x^2-3809x+82431$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.1, 228.24.0.?, 456.48.0.?
44688.j2	44688g2	44688.j	44688g	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{2} \cdot 7^{10} \cdot 19^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$3192$	$48$	$0$	$1$	$1$		$3$	$245760$	$1.614981$	$93280467172/7800849$	$[0, -1, 0, -46664, 3604224]$	$y^2=x^3-x^2-46664x+3604224$	2.6.0.a.1, 8.12.0.b.1, 28.12.0-2.a.1.1, 56.24.0-8.b.1.1, 228.12.0.?, $\ldots$
60648.bm2	60648o2	60648.bm	60648o	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{2} \cdot 7^{4} \cdot 19^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$456$	$48$	$0$	$21.98331186$	$1$		$3$	$921600$	$2.114246$	$93280467172/7800849$	$[0, 1, 0, -343792, -71877520]$	$y^2=x^3+x^2-343792x-71877520$	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.3, 76.12.0.?, $\ldots$
67032.ci2	67032bf2	67032.ci	67032bf	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{8} \cdot 7^{10} \cdot 19^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$3192$	$48$	$0$	$1$	$4$	$2$	$3$	$983040$	$2.164288$	$93280467172/7800849$	$[0, 0, 0, -419979, 96894070]$	$y^2=x^3-419979x+96894070$	2.6.0.a.1, 8.12.0.b.1, 84.12.0.?, 168.24.0.?, 228.12.0.?, $\ldots$
76608.ed2	76608bv2	76608.ed	76608bv	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{16} \cdot 3^{8} \cdot 7^{4} \cdot 19^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$456$	$48$	$0$	$5.328073573$	$1$		$3$	$327680$	$1.537905$	$93280467172/7800849$	$[0, 0, 0, -34284, -2259920]$	$y^2=x^3-34284x-2259920$	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.1, 76.12.0.?, $\ldots$
76608.fd2	76608ey2	76608.fd	76608ey	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ 2^{16} \cdot 3^{8} \cdot 7^{4} \cdot 19^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$456$	$48$	$0$	$1$	$1$		$3$	$327680$	$1.537905$	$93280467172/7800849$	$[0, 0, 0, -34284, 2259920]$	$y^2=x^3-34284x+2259920$	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.2, 76.12.0.?, $\ldots$
79800.bn2	79800k2	79800.bn	79800k	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$2280$	$48$	$0$	$1.927058340$	$1$		$7$	$327680$	$1.446743$	$93280467172/7800849$	$[0, 1, 0, -23808, 1299888]$	$y^2=x^3+x^2-23808x+1299888$	2.6.0.a.1, 8.12.0.b.1, 20.12.0-2.a.1.1, 40.24.0-8.b.1.2, 228.12.0.?, $\ldots$
121296.bq2	121296r2	121296.bq	121296r	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{2} \cdot 7^{4} \cdot 19^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$456$	$48$	$0$	$3.764780146$	$1$		$5$	$1843200$	$2.114246$	$93280467172/7800849$	$[0, -1, 0, -343792, 71877520]$	$y^2=x^3-x^2-343792x+71877520$	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.3, 76.12.0.?, $\ldots$
134064.er2	134064ex2	134064.er	134064ex	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ 2^{10} \cdot 3^{8} \cdot 7^{10} \cdot 19^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$3192$	$48$	$0$	$5.493662317$	$1$		$5$	$1966080$	$2.164288$	$93280467172/7800849$	$[0, 0, 0, -419979, -96894070]$	$y^2=x^3-419979x-96894070$	2.6.0.a.1, 8.12.0.b.1, 84.12.0.?, 168.24.0.?, 228.12.0.?, $\ldots$
159600.bq2	159600gz2	159600.bq	159600gz	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$2280$	$48$	$0$	$1$	$1$		$3$	$655360$	$1.446743$	$93280467172/7800849$	$[0, -1, 0, -23808, -1299888]$	$y^2=x^3-x^2-23808x-1299888$	2.6.0.a.1, 8.12.0.b.1, 20.12.0-2.a.1.1, 40.24.0-8.b.1.1, 228.12.0.?, $\ldots$
178752.ep2	178752kg2	178752.ep	178752kg	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{16} \cdot 3^{2} \cdot 7^{10} \cdot 19^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$3192$	$48$	$0$	$14.25370695$	$1$		$13$	$1966080$	$1.961554$	$93280467172/7800849$	$[0, -1, 0, -186657, -28647135]$	$y^2=x^3-x^2-186657x-28647135$	2.6.0.a.1, 8.12.0.b.1, 28.12.0-2.a.1.1, 56.24.0-8.b.1.1, 228.12.0.?, $\ldots$
178752.jd2	178752ce2	178752.jd	178752ce	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ 2^{16} \cdot 3^{2} \cdot 7^{10} \cdot 19^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$3192$	$48$	$0$	$6.466148650$	$1$		$5$	$1966080$	$1.961554$	$93280467172/7800849$	$[0, 1, 0, -186657, 28647135]$	$y^2=x^3+x^2-186657x+28647135$	2.6.0.a.1, 8.12.0.b.1, 28.12.0-2.a.1.1, 56.24.0-8.b.1.2, 228.12.0.?, $\ldots$
181944.j2	181944d2	181944.j	181944d	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{8} \cdot 7^{4} \cdot 19^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.6	2Cs	$456$	$48$	$0$	$1$	$4$	$2$	$3$	$7372800$	$2.663551$	$93280467172/7800849$	$[0, 0, 0, -3094131, 1937598910]$	$y^2=x^3-3094131x+1937598910$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.3, 228.24.0.?, 456.48.0.?
239400.ej2	239400ej2	239400.ej	239400ej	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{8} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$2280$	$48$	$0$	$1$	$1$		$3$	$2621440$	$1.996050$	$93280467172/7800849$	$[0, 0, 0, -214275, -35311250]$	$y^2=x^3-214275x-35311250$	2.6.0.a.1, 8.12.0.b.1, 60.12.0-2.a.1.1, 120.24.0.?, 228.12.0.?, $\ldots$
363888.r2	363888r2	363888.r	363888r	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ 2^{10} \cdot 3^{8} \cdot 7^{4} \cdot 19^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.6	2Cs	$456$	$48$	$0$	$1$	$1$		$3$	$14745600$	$2.663551$	$93280467172/7800849$	$[0, 0, 0, -3094131, -1937598910]$	$y^2=x^3-3094131x-1937598910$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.3, 228.24.0.?, 456.48.0.?
386232.bc2	386232bc2	386232.bc	386232bc	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 $	$ 2^{10} \cdot 3^{2} \cdot 7^{4} \cdot 11^{6} \cdot 19^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$5016$	$48$	$0$	$1$	$1$		$3$	$3276800$	$1.840973$	$93280467172/7800849$	$[0, -1, 0, -115232, -13887300]$	$y^2=x^3-x^2-115232x-13887300$	2.6.0.a.1, 8.12.0.b.1, 44.12.0-2.a.1.1, 88.24.0.?, 228.12.0.?, $\ldots$
424536.h2	424536h2	424536.h	424536h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} $	$ 2^{10} \cdot 3^{2} \cdot 7^{10} \cdot 19^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$3192$	$48$	$0$	$4.654076811$	$1$		$5$	$44236800$	$3.087200$	$93280467172/7800849$	$[0, -1, 0, -16845824, 24620297724]$	$y^2=x^3-x^2-16845824x+24620297724$	2.6.0.a.1, 8.12.0.b.1, 84.12.0.?, 168.24.0.?, 228.12.0.?, $\ldots$
478800.bj2	478800bj2	478800.bj	478800bj	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ 2^{10} \cdot 3^{8} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$2280$	$48$	$0$	$1.561460715$	$1$		$13$	$5242880$	$1.996050$	$93280467172/7800849$	$[0, 0, 0, -214275, 35311250]$	$y^2=x^3-214275x+35311250$	2.6.0.a.1, 8.12.0.b.1, 60.12.0-2.a.1.1, 120.24.0.?, 228.12.0.?, $\ldots$
485184.q2	485184q2	485184.q	485184q	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{16} \cdot 3^{2} \cdot 7^{4} \cdot 19^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$456$	$48$	$0$	$1$	$1$		$3$	$14745600$	$2.460819$	$93280467172/7800849$	$[0, -1, 0, -1375169, -573644991]$	$y^2=x^3-x^2-1375169x-573644991$	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.2, 24.24.0-8.b.1.4, 76.12.0.?, $\ldots$
485184.fq2	485184fq2	485184.fq	485184fq	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ 2^{16} \cdot 3^{2} \cdot 7^{4} \cdot 19^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.4	2Cs	$456$	$48$	$0$	$4.482798507$	$1$		$5$	$14745600$	$2.460819$	$93280467172/7800849$	$[0, 1, 0, -1375169, 573644991]$	$y^2=x^3+x^2-1375169x+573644991$	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.2, 24.24.0-8.b.1.4, 76.12.0.?, $\ldots$

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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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