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 (23 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	Semistable	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
3570.t3	3570t3	3570.t	3570t	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{4} \cdot 5^{4} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.48.0.32	2Cs	$2040$	$192$	$1$	$1$	$1$		$2$	$36864$	$1.788086$	$146796951366228945601/5397929064360000$	$0.99129$	$5.67650$	$[1, 1, 1, -109900, -13616083]$	$y^2+xy+y=x^3+x^2-109900x-13616083$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.e.2.4, 120.96.0.?, 136.96.0.?, $\ldots$	$[ ]$
10710.a3	10710f4	10710.a	10710f	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$2040$	$192$	$1$	$1$	$1$		$2$	$294912$	$2.337391$	$146796951366228945601/5397929064360000$	$0.99129$	$5.71480$	$[1, -1, 0, -989100, 366645136]$	$y^2+xy=x^3-x^2-989100x+366645136$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 12.24.0-4.b.1.1, 24.48.0-8.e.2.1, $\ldots$	$[ ]$
17850.ba3	17850u3	17850.ba	17850u	$6$	$8$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{4} \cdot 5^{10} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$2040$	$192$	$1$	$1.265897258$	$1$		$12$	$884736$	$2.592804$	$146796951366228945601/5397929064360000$	$0.99129$	$5.72968$	$[1, 0, 1, -2747501, -1696515352]$	$y^2+xy+y=x^3-2747501x-1696515352$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 20.24.0-4.b.1.1, 24.48.0-8.e.2.8, $\ldots$	$[(-837, 4534)]$
24990.ca3	24990by3	24990.ca	24990by	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{4} \cdot 5^{4} \cdot 7^{14} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$14280$	$192$	$1$	$1$	$1$		$2$	$1769472$	$2.761040$	$146796951366228945601/5397929064360000$	$0.99129$	$5.73866$	$[1, 0, 0, -5385101, 4654161105]$	$y^2+xy=x^3-5385101x+4654161105$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 28.24.0-4.b.1.1, 56.48.0-8.e.2.1, $\ldots$	$[ ]$
28560.ds3	28560ef3	28560.ds	28560ef	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ 2^{18} \cdot 3^{4} \cdot 5^{4} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.24	2Cs	$2040$	$192$	$1$	$1$	$1$		$7$	$884736$	$2.481232$	$146796951366228945601/5397929064360000$	$0.99129$	$5.33671$	$[0, 1, 0, -1758400, 867912500]$	$y^2=x^3+x^2-1758400x+867912500$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.e.2.2, 120.96.0.?, 136.96.0.?, $\ldots$	$[ ]$
53550.du3	53550eb3	53550.du	53550eb	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{6} \cdot 3^{10} \cdot 5^{10} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.66	2Cs	$2040$	$192$	$1$	$0.838446074$	$1$		$16$	$7077888$	$3.142109$	$146796951366228945601/5397929064360000$	$0.99129$	$5.75696$	$[1, -1, 1, -24727505, 45805914497]$	$y^2+xy+y=x^3-x^2-24727505x+45805914497$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.2.6, 60.24.0-4.b.1.1, 120.96.0.?, $\ldots$	$[(1629, 98410)]$
60690.bv3	60690bw3	60690.bv	60690bw	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} $	$ 2^{6} \cdot 3^{4} \cdot 5^{4} \cdot 7^{8} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.93	2Cs	$2040$	$192$	$1$	$1$	$1$		$2$	$10616832$	$3.204693$	$146796951366228945601/5397929064360000$	$0.99129$	$5.75972$	$[1, 0, 0, -31761106, -66673487164]$	$y^2+xy=x^3-31761106x-66673487164$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.2.14, 68.24.0-4.b.1.1, 120.96.0.?, $\ldots$	$[ ]$
74970.bd3	74970by3	74970.bd	74970by	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{10} \cdot 5^{4} \cdot 7^{14} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$14280$	$192$	$1$	$4.173644526$	$1$		$8$	$14155776$	$3.310345$	$146796951366228945601/5397929064360000$	$0.99129$	$5.76424$	$[1, -1, 0, -48465909, -125662349835]$	$y^2+xy=x^3-x^2-48465909x-125662349835$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 84.24.0.?, 120.48.0.?, $\ldots$	$[(8061, 82032)]$
85680.db3	85680el3	85680.db	85680el	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ 2^{18} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$2040$	$192$	$1$	$1$	$1$		$3$	$7077888$	$3.030540$	$146796951366228945601/5397929064360000$	$0.99129$	$5.40086$	$[0, 0, 0, -15825603, -23449463102]$	$y^2=x^3-15825603x-23449463102$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 12.24.0-4.b.1.3, 24.48.0-8.e.2.3, $\ldots$	$[ ]$
114240.cp3	114240gl3	114240.cp	114240gl	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ 2^{24} \cdot 3^{4} \cdot 5^{4} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.85	2Cs	$2040$	$192$	$1$	$1$	$1$		$3$	$7077888$	$2.827805$	$146796951366228945601/5397929064360000$	$0.99129$	$5.05856$	$[0, -1, 0, -7033601, 6950333601]$	$y^2=x^3-x^2-7033601x+6950333601$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.2.3, 68.24.0-4.b.1.2, 120.96.0.?, $\ldots$	$[ ]$
114240.fq3	114240dk3	114240.fq	114240dk	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ 2^{24} \cdot 3^{4} \cdot 5^{4} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.94	2Cs	$2040$	$192$	$1$	$7.019781990$	$1$		$5$	$7077888$	$2.827805$	$146796951366228945601/5397929064360000$	$0.99129$	$5.05856$	$[0, 1, 0, -7033601, -6950333601]$	$y^2=x^3+x^2-7033601x-6950333601$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.2.1, 68.24.0-4.b.1.2, 120.96.0.?, $\ldots$	$[(23787, 3644928)]$
124950.ce3	124950bc3	124950.ce	124950bc	$6$	$8$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{4} \cdot 5^{10} \cdot 7^{14} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$14280$	$192$	$1$	$9.207051086$	$1$		$2$	$42467328$	$3.565758$	$146796951366228945601/5397929064360000$	$0.99129$	$5.77450$	$[1, 1, 0, -134627525, 581770138125]$	$y^2+xy=x^3+x^2-134627525x+581770138125$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 120.48.0.?, 136.48.0.?, $\ldots$	$[(1178485/12, 283129715/12)]$
142800.b3	142800ei3	142800.b	142800ei	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{18} \cdot 3^{4} \cdot 5^{10} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$2040$	$192$	$1$	$1$	$1$		$3$	$21233664$	$3.285950$	$146796951366228945601/5397929064360000$	$0.99129$	$5.42665$	$[0, -1, 0, -43960008, 108576982512]$	$y^2=x^3-x^2-43960008x+108576982512$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 20.24.0-4.b.1.3, 24.48.0-8.e.2.6, $\ldots$	$[ ]$
182070.bw3	182070ct3	182070.bw	182070ct	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17^{2} $	$ 2^{6} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$2040$	$192$	$1$	$1$	$1$		$2$	$84934656$	$3.753998$	$146796951366228945601/5397929064360000$	$0.99129$	$5.78151$	$[1, -1, 0, -285849954, 1800184153428]$	$y^2+xy=x^3-x^2-285849954x+1800184153428$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0-8.e.2.15, 40.48.0-8.e.2.11, $\ldots$	$[ ]$
199920.c3	199920cy4	199920.c	199920cy	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 $	$ 2^{18} \cdot 3^{4} \cdot 5^{4} \cdot 7^{14} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$14280$	$192$	$1$	$7.123502252$	$1$		$5$	$42467328$	$3.454189$	$146796951366228945601/5397929064360000$	$0.99129$	$5.44245$	$[0, -1, 0, -86161616, -297866310720]$	$y^2=x^3-x^2-86161616x-297866310720$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 28.24.0-4.b.1.3, 56.48.0-8.e.2.3, $\ldots$	$[(31898, 5422950)]$
303450.b3	303450b4	303450.b	303450b	$6$	$8$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17^{2} $	$ 2^{6} \cdot 3^{4} \cdot 5^{10} \cdot 7^{8} \cdot 17^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$2040$	$192$	$1$	$11.39520485$	$1$		$2$	$254803968$	$4.009415$	$146796951366228945601/5397929064360000$	$0.99129$	$5.79035$	$[1, 1, 0, -794027650, -8334185895500]$	$y^2+xy=x^3+x^2-794027650x-8334185895500$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0-8.e.2.10, 40.48.0-8.e.2.14, $\ldots$	$[(36469705/9, 219635468515/9)]$
342720.ld3	342720ld3	342720.ld	342720ld	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ 2^{24} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$2040$	$192$	$1$	$5.117216781$	$1$		$5$	$56623104$	$3.377113$	$146796951366228945601/5397929064360000$	$0.99129$	$5.13971$	$[0, 0, 0, -63302412, 187595704816]$	$y^2=x^3-63302412x+187595704816$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0-8.e.2.4, 40.48.0-8.e.2.8, $\ldots$	$[(-3388, 602640)]$
342720.md3	342720md4	342720.md	342720md	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ 2^{24} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$2040$	$192$	$1$	$2.360253907$	$1$		$9$	$56623104$	$3.377113$	$146796951366228945601/5397929064360000$	$0.99129$	$5.13971$	$[0, 0, 0, -63302412, -187595704816]$	$y^2=x^3-63302412x-187595704816$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0-8.e.2.2, 40.48.0-8.e.2.6, $\ldots$	$[(9868, 385560)]$
374850.jf3	374850jf4	374850.jf	374850jf	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ 2^{6} \cdot 3^{10} \cdot 5^{10} \cdot 7^{14} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$14280$	$192$	$1$	$1$	$4$	$2$	$2$	$339738624$	$4.115067$	$146796951366228945601/5397929064360000$	$0.99129$	$5.79381$	$[1, -1, 1, -1211647730, -15709005377103]$	$y^2+xy+y=x^3-x^2-1211647730x-15709005377103$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 56.48.0-8.e.2.8, 120.48.0.?, $\ldots$	$[ ]$
424830.fi3	424830fi3	424830.fi	424830fi	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} $	$ 2^{6} \cdot 3^{4} \cdot 5^{4} \cdot 7^{14} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$14280$	$192$	$1$	$1$	$1$		$2$	$509607936$	$4.177650$	$146796951366228945601/5397929064360000$	$0.99129$	$5.79580$	$[1, 1, 1, -1556294195, 22867449803057]$	$y^2+xy+y=x^3+x^2-1556294195x+22867449803057$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 56.48.0-8.e.2.15, 120.48.0.?, $\ldots$	$[ ]$
428400.gi3	428400gi4	428400.gi	428400gi	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 $	$ 2^{18} \cdot 3^{10} \cdot 5^{10} \cdot 7^{8} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.90	2Cs	$2040$	$192$	$1$	$1$	$4$	$2$	$3$	$169869312$	$3.835258$	$146796951366228945601/5397929064360000$	$0.99129$	$5.47522$	$[0, 0, 0, -395640075, -2931182887750]$	$y^2=x^3-395640075x-2931182887750$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.2.8, 60.24.0-4.b.1.3, 120.96.0.?, $\ldots$	$[ ]$
431970.y3	431970y3	431970.y	431970y	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 17 $	$ 2^{6} \cdot 3^{4} \cdot 5^{4} \cdot 7^{8} \cdot 11^{6} \cdot 17^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.10	2Cs	$22440$	$192$	$1$	$1.267733866$	$1$		$38$	$47185920$	$2.987034$	$146796951366228945601/5397929064360000$	$0.99129$	$4.68730$	$[1, 1, 0, -13297902, 18056516724]$	$y^2+xy=x^3+x^2-13297902x+18056516724$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 44.24.0-4.b.1.1, 88.48.0.?, $\ldots$	$[(1733, 13956), (1348, 50146)]$
485520.bg3	485520bg3	485520.bg	485520bg	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} $	$ 2^{18} \cdot 3^{4} \cdot 5^{4} \cdot 7^{8} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.84	2Cs	$2040$	$192$	$1$	$1$	$4$	$2$	$3$	$254803968$	$3.897839$	$146796951366228945601/5397929064360000$	$0.99129$	$5.48024$	$[0, -1, 0, -508177696, 4267103178496]$	$y^2=x^3-x^2-508177696x+4267103178496$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.2.16, 68.24.0-4.b.1.3, 120.96.0.?, $\ldots$	$[ ]$

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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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