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 (29 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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1122.d2	1122d1	1122.d	1122d	$2$	$2$	$ 2 \cdot 3 \cdot 11 \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.171570029$	$1$	$13$	$672$	$0.443193$	$18052771191337/444958272$	$0.94100$	$4.34642$	$[1, 0, 1, -547, 4766]$	$y^2+xy+y=x^3-547x+4766$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(7, 32)]$
3366.p2	3366n1	3366.p	3366n	$2$	$2$	$ 2 \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{6} \cdot 3^{13} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$5376$	$0.992499$	$18052771191337/444958272$	$0.94100$	$4.57010$	$[1, -1, 1, -4919, -128689]$	$y^2+xy+y=x^3-x^2-4919x-128689$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
8976.e2	8976p1	8976.e	8976p	$2$	$2$	$ 2^{4} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{18} \cdot 3^{7} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$16128$	$1.136341$	$18052771191337/444958272$	$0.94100$	$4.26728$	$[0, -1, 0, -8744, -305040]$	$y^2=x^3-x^2-8744x-305040$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
12342.ba2	12342bf1	12342.ba	12342bf	$2$	$2$	$ 2 \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 11^{7} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.313080160$	$1$	$11$	$80640$	$1.642141$	$18052771191337/444958272$	$0.94100$	$4.76731$	$[1, 0, 0, -66129, -6410007]$	$y^2+xy=x^3-66129x-6410007$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-144, 435)]$
19074.d2	19074a1	19074.d	19074a	$2$	$2$	$ 2 \cdot 3 \cdot 11 \cdot 17^{2} $	$ 2^{6} \cdot 3^{7} \cdot 11 \cdot 17^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$5.122628666$	$1$	$3$	$193536$	$1.859800$	$18052771191337/444958272$	$0.94100$	$4.82175$	$[1, 1, 0, -157944, 23574528]$	$y^2+xy=x^3+x^2-157944x+23574528$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-136, 6592)]$
26928.bu2	26928bw1	26928.bu	26928bw	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{18} \cdot 3^{13} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1.766302479$	$1$	$5$	$129024$	$1.685646$	$18052771191337/444958272$	$0.94100$	$4.45389$	$[0, 0, 0, -78699, 8314778]$	$y^2=x^3-78699x+8314778$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(31, 2430)]$
28050.cr2	28050ci1	28050.cr	28050ci	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 5^{6} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$86016$	$1.247913$	$18052771191337/444958272$	$0.94100$	$3.92325$	$[1, 1, 1, -13663, 595781]$	$y^2+xy+y=x^3+x^2-13663x+595781$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
35904.bc2	35904f1	35904.bc	35904f	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{24} \cdot 3^{7} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$3.885435648$	$1$	$3$	$129024$	$1.482914$	$18052771191337/444958272$	$0.94100$	$4.09978$	$[0, -1, 0, -34977, 2475297]$	$y^2=x^3-x^2-34977x+2475297$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-32, 1887)]$
35904.dd2	35904cw1	35904.dd	35904cw	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{24} \cdot 3^{7} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$129024$	$1.482914$	$18052771191337/444958272$	$0.94100$	$4.09978$	$[0, 1, 0, -34977, -2475297]$	$y^2=x^3+x^2-34977x-2475297$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
37026.p2	37026k1	37026.p	37026k	$2$	$2$	$ 2 \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{6} \cdot 3^{13} \cdot 11^{7} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$4.595555912$	$1$	$3$	$645120$	$2.191448$	$18052771191337/444958272$	$0.94100$	$4.89605$	$[1, -1, 0, -595161, 173070189]$	$y^2+xy=x^3-x^2-595161x+173070189$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-150, 16167)]$
54978.m2	54978l1	54978.m	54978l	$2$	$2$	$ 2 \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 7^{6} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$241920$	$1.416149$	$18052771191337/444958272$	$0.94100$	$3.86633$	$[1, 1, 0, -26779, -1661603]$	$y^2+xy=x^3+x^2-26779x-1661603$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
57222.bj2	57222bv1	57222.bj	57222bv	$2$	$2$	$ 2 \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{6} \cdot 3^{13} \cdot 11 \cdot 17^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$1548288$	$2.409107$	$18052771191337/444958272$	$0.94100$	$4.93992$	$[1, -1, 1, -1421501, -637933755]$	$y^2+xy+y=x^3-x^2-1421501x-637933755$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
84150.cn2	84150be1	84150.cn	84150be	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{6} \cdot 3^{13} \cdot 5^{6} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$688128$	$1.797218$	$18052771191337/444958272$	$0.94100$	$4.12444$	$[1, -1, 0, -122967, -16209059]$	$y^2+xy=x^3-x^2-122967x-16209059$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
98736.h2	98736cq1	98736.h	98736cq	$2$	$2$	$ 2^{4} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{18} \cdot 3^{7} \cdot 11^{7} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$1935360$	$2.335289$	$18052771191337/444958272$	$0.94100$	$4.62857$	$[0, -1, 0, -1058064, 410240448]$	$y^2=x^3-x^2-1058064x+410240448$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
107712.s2	107712cn1	107712.s	107712cn	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{24} \cdot 3^{13} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$1032192$	$2.032219$	$18052771191337/444958272$	$0.94100$	$4.27994$	$[0, 0, 0, -314796, -66518224]$	$y^2=x^3-314796x-66518224$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
107712.bl2	107712dz1	107712.bl	107712dz	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{24} \cdot 3^{13} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$1032192$	$2.032219$	$18052771191337/444958272$	$0.94100$	$4.27994$	$[0, 0, 0, -314796, 66518224]$	$y^2=x^3-314796x+66518224$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
152592.cw2	152592y1	152592.cw	152592y	$2$	$2$	$ 2^{4} \cdot 3 \cdot 11 \cdot 17^{2} $	$ 2^{18} \cdot 3^{7} \cdot 11 \cdot 17^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$4644864$	$2.552948$	$18052771191337/444958272$	$0.94100$	$4.67859$	$[0, 1, 0, -2527112, -1513824012]$	$y^2=x^3+x^2-2527112x-1513824012$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
164934.cb2	164934g1	164934.cb	164934g	$2$	$2$	$ 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \cdot 17 $	$ 2^{6} \cdot 3^{13} \cdot 7^{6} \cdot 11 \cdot 17^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1.996653512$	$1$	$21$	$1935360$	$1.965454$	$18052771191337/444958272$	$0.94100$	$4.06145$	$[1, -1, 1, -241016, 44622267]$	$y^2+xy+y=x^3-x^2-241016x+44622267$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(419, 3921), (-67, 7809)]$
189618.bs2	189618k1	189618.bs	189618k	$2$	$2$	$ 2 \cdot 3 \cdot 11 \cdot 13^{2} \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 11 \cdot 13^{6} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.938693790$	$1$	$7$	$1580544$	$1.725668$	$18052771191337/444958272$	$0.94100$	$3.77807$	$[1, 0, 0, -92362, 10563812]$	$y^2+xy=x^3-92362x+10563812$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(128, 854)]$
209814.cm2	209814bg1	209814.cm	209814bg	$2$	$2$	$ 2 \cdot 3 \cdot 11^{2} \cdot 17^{2} $	$ 2^{6} \cdot 3^{7} \cdot 11^{7} \cdot 17^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$11.82842808$	$1$	$1$	$23224320$	$3.058746$	$18052771191337/444958272$	$0.94100$	$5.05232$	$[1, 1, 1, -19111287, -31473253107]$	$y^2+xy+y=x^3+x^2-19111287x-31473253107$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-8498709/55, 1451888846/55)]$
224400.fk2	224400bs1	224400.fk	224400bs	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{18} \cdot 3^{7} \cdot 5^{6} \cdot 11 \cdot 17^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.565654590$	$1$	$19$	$2064384$	$1.941059$	$18052771191337/444958272$	$0.94100$	$3.93621$	$[0, 1, 0, -218608, -38567212]$	$y^2=x^3+x^2-218608x-38567212$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-268, 918), (-238, 192)]$
296208.ek2	296208ek1	296208.ek	296208ek	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{18} \cdot 3^{13} \cdot 11^{7} \cdot 17^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$6.067481347$	$1$	$11$	$15482880$	$2.884594$	$18052771191337/444958272$	$0.94100$	$4.74815$	$[0, 0, 0, -9522579, -11066969518]$	$y^2=x^3-9522579x-11066969518$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-1799, 15552), (-1969, 7018)]$
308550.t2	308550t1	308550.t	308550t	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 17 $	$ 2^{6} \cdot 3^{7} \cdot 5^{6} \cdot 11^{7} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$10321920$	$2.446861$	$18052771191337/444958272$	$0.94100$	$4.31724$	$[1, 1, 0, -1653225, -801250875]$	$y^2+xy=x^3+x^2-1653225x-801250875$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
394944.ea2	394944ea1	394944.ea	394944ea	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{24} \cdot 3^{7} \cdot 11^{7} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$23.22166718$	$1$	$1$	$15482880$	$2.681862$	$18052771191337/444958272$	$0.94100$	$4.45337$	$[0, -1, 0, -4232257, -3277691327]$	$y^2=x^3-x^2-4232257x-3277691327$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(-108993298917/10061, 5565329784150380/10061)]$
394944.ig2	394944ig1	394944.ig	394944ig	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{24} \cdot 3^{7} \cdot 11^{7} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1.171307282$	$1$	$5$	$15482880$	$2.681862$	$18052771191337/444958272$	$0.94100$	$4.45337$	$[0, 1, 0, -4232257, 3277691327]$	$y^2=x^3+x^2-4232257x+3277691327$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(1514, 18513)]$
405042.ca2	405042ca1	405042.ca	405042ca	$2$	$2$	$ 2 \cdot 3 \cdot 11 \cdot 17 \cdot 19^{2} $	$ 2^{6} \cdot 3^{7} \cdot 11 \cdot 17^{2} \cdot 19^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$4402944$	$1.915413$	$18052771191337/444958272$	$0.94100$	$3.73233$	$[1, 1, 1, -197294, -33086293]$	$y^2+xy+y=x^3+x^2-197294x-33086293$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[]$
439824.fs2	439824fs1	439824.fs	439824fs	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 $	$ 2^{18} \cdot 3^{7} \cdot 7^{6} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1.567745168$	$1$	$7$	$5806080$	$2.109295$	$18052771191337/444958272$	$0.94100$	$3.88772$	$[0, 1, 0, -428472, 105485652]$	$y^2=x^3+x^2-428472x+105485652$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(324, 882)]$
457776.z2	457776z1	457776.z	457776z	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{18} \cdot 3^{13} \cdot 11 \cdot 17^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$4.844697277$	$1$	$3$	$37158912$	$3.102253$	$18052771191337/444958272$	$0.94100$	$4.78996$	$[0, 0, 0, -22744011, 40850504314]$	$y^2=x^3-22744011x+40850504314$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(26486, 4244832)]$
476850.ir2	476850ir1	476850.ir	476850ir	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17^{2} $	$ 2^{6} \cdot 3^{7} \cdot 5^{6} \cdot 11 \cdot 17^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1.024315091$	$1$	$9$	$24772608$	$2.664520$	$18052771191337/444958272$	$0.94100$	$4.37326$	$[1, 0, 0, -3948613, 2954713217]$	$y^2+xy=x^3-3948613x+2954713217$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(2132, 63959)]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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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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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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