Elliptic curve search results

Results (1-50 of 1887132 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	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
37.a1	37a1	37.a	37a	$1$	$1$	\( 37 \)	\( 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.051111408$	$1$		$10$	$2$	$-0.996542$	$110592/37$	$[0, 0, 1, -1, 0]$	\(y^2+y=x^3-x\)
43.a1	43a1	43.a	43a	$1$	$1$	\( 43 \)	\( -43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.062816507$	$1$		$10$	$2$	$-1.004431$	$-4096/43$	$[0, 1, 1, 0, 0]$	\(y^2+y=x^3+x^2\)
53.a1	53a1	53.a	53a	$1$	$1$	\( 53 \)	\( -53 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.092981484$	$1$		$8$	$2$	$-0.988547$	$3375/53$	$[1, -1, 1, 0, 0]$	\(y^2+xy+y=x^3-x^2\)
57.a1	57a1	57.a	57a	$1$	$1$	\( 3 \cdot 19 \)	\( - 3^{2} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.037574592$	$1$		$12$	$4$	$-0.836549$	$-1404928/171$	$[0, -1, 1, -2, 2]$	\(y^2+y=x^3-x^2-2x+2\)
58.a1	58a1	58.a	58a	$1$	$1$	\( 2 \cdot 29 \)	\( - 2^{2} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.042420307$	$1$		$12$	$4$	$-0.902228$	$-185193/116$	$[1, -1, 0, -1, 1]$	\(y^2+xy=x^3-x^2-x+1\)
61.a1	61a1	61.a	61a	$1$	$1$	\( 61 \)	\( -61 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.079187731$	$1$		$8$	$2$	$-0.905458$	$-912673/61$	$[1, 0, 0, -2, 1]$	\(y^2+xy=x^3-2x+1\)
65.a1	65a1	65.a	65a	$2$	$2$	\( 5 \cdot 13 \)	\( 5 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.22	2B	$0.375514098$	$1$		$7$	$2$	$-0.961616$	$117649/65$	$[1, 0, 0, -1, 0]$	\(y^2+xy=x^3-x\)
65.a2	65a2	65.a	65a	$2$	$2$	\( 5 \cdot 13 \)	\( - 5^{2} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.37	2B	$0.187757049$	$1$		$12$	$4$	$-0.615042$	$6967871/4225$	$[1, 0, 0, 4, 1]$	\(y^2+xy=x^3+4x+1\)
77.a1	77a1	77.a	77a	$1$	$1$	\( 7 \cdot 11 \)	\( - 7^{2} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.098027979$	$1$		$8$	$4$	$-0.786654$	$884736/539$	$[0, 0, 1, 2, 0]$	\(y^2+y=x^3+2x\)
79.a1	79a1	79.a	79a	$1$	$1$	\( 79 \)	\( 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.097664210$	$1$		$8$	$2$	$-0.895041$	$912673/79$	$[1, 1, 1, -2, 0]$	\(y^2+xy+y=x^3+x^2-2x\)
82.a1	82a2	82.a	82a	$2$	$2$	\( 2 \cdot 41 \)	\( 2 \cdot 41^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.6	2B	$0.449413849$	$1$		$6$	$8$	$-0.531580$	$169112377/3362$	$[1, 0, 1, -12, -16]$	\(y^2+xy+y=x^3-12x-16\)
82.a2	82a1	82.a	82a	$2$	$2$	\( 2 \cdot 41 \)	\( 2^{2} \cdot 41 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.1	2B	$0.224706924$	$1$		$11$	$4$	$-0.878154$	$389017/164$	$[1, 0, 1, -2, 0]$	\(y^2+xy+y=x^3-2x\)
83.a1	83a1	83.a	83a	$1$	$1$	\( 83 \)	\( -83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.177292294$	$1$		$6$	$2$	$-0.943868$	$103823/83$	$[1, 1, 1, 1, 0]$	\(y^2+xy+y=x^3+x^2+x\)
88.a1	88a1	88.a	88a	$1$	$1$	\( 2^{3} \cdot 11 \)	\( - 2^{8} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.040264364$	$1$		$14$	$8$	$-0.629211$	$-27648/11$	$[0, 0, 0, -4, 4]$	\(y^2=x^3-4x+4\)
89.a1	89a1	89.a	89a	$1$	$1$	\( 89 \)	\( -89 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.112104881$	$1$		$6$	$2$	$-0.926876$	$-117649/89$	$[1, 1, 1, -1, 0]$	\(y^2+xy+y=x^3+x^2-x\)
91.a1	91a1	91.a	91a	$1$	$1$	\( 7 \cdot 13 \)	\( - 7 \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.142392150$	$1$		$6$	$4$	$-0.936330$	$110592/91$	$[0, 0, 1, 1, 0]$	\(y^2+y=x^3+x\)
91.b1	91b3	91.b	91b	$3$	$9$	\( 7 \cdot 13 \)	\( - 7^{9} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.24.0.3	3B.1.2	$0.117693898$	$1$		$10$	$36$	$0.360104$	$-178643795968/524596891$	$[0, 1, 1, -117, -1245]$	\(y^2+y=x^3+x^2-117x-1245\)
91.b2	91b1	91.b	91b	$3$	$9$	\( 7 \cdot 13 \)	\( - 7 \cdot 13 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.24.0.1	3B.1.1	$1.059245086$	$1$		$6$	$4$	$-0.738508$	$-43614208/91$	$[0, 1, 1, -7, 5]$	\(y^2+y=x^3+x^2-7x+5\)
91.b3	91b2	91.b	91b	$3$	$9$	\( 7 \cdot 13 \)	\( - 7^{3} \cdot 13^{3} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.24.0.1	3Cs.1.1	$0.353081695$	$1$		$10$	$12$	$-0.189202$	$224755712/753571$	$[0, 1, 1, 13, 42]$	\(y^2+y=x^3+x^2+13x+42\)
92.a1	92b1	92.a	92b	$1$	$1$	\( 2^{2} \cdot 23 \)	\( - 2^{4} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.049808397$	$1$		$12$	$6$	$-0.821413$	$-6912/23$	$[0, 0, 0, -1, 1]$	\(y^2=x^3-x+1\)
99.a1	99a2	99.a	99a	$2$	$2$	\( 3^{2} \cdot 11 \)	\( 3^{3} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.151285692$	$1$		$10$	$8$	$-0.488690$	$19034163/121$	$[1, -1, 1, -17, 30]$	\(y^2+xy+y=x^3-x^2-17x+30\)
99.a2	99a1	99.a	99a	$2$	$2$	\( 3^{2} \cdot 11 \)	\( 3^{3} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.302571384$	$1$		$9$	$4$	$-0.835264$	$19683/11$	$[1, -1, 1, -2, 0]$	\(y^2+xy+y=x^3-x^2-2x\)
101.a1	101a1	101.a	101a	$1$	$1$	\( 101 \)	\( 101 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.164703452$	$1$		$6$	$2$	$-0.916363$	$262144/101$	$[0, 1, 1, -1, -1]$	\(y^2+y=x^3+x^2-x-1\)
102.a1	102a1	102.a	102a	$2$	$2$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{2} \cdot 3^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.4	2B	$0.143253892$	$1$		$15$	$8$	$-0.763528$	$1771561/612$	$[1, 1, 0, -2, 0]$	\(y^2+xy=x^3+x^2-2x\)
102.a2	102a2	102.a	102a	$2$	$2$	\( 2 \cdot 3 \cdot 17 \)	\( - 2 \cdot 3^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$0.286507785$	$1$		$8$	$16$	$-0.416955$	$46268279/46818$	$[1, 1, 0, 8, 10]$	\(y^2+xy=x^3+x^2+8x+10\)
106.a1	106b1	106.a	106b	$1$	$1$	\( 2 \cdot 53 \)	\( - 2^{4} \cdot 53 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.068912680$	$1$		$10$	$8$	$-0.641726$	$-47045881/848$	$[1, 1, 0, -7, 5]$	\(y^2+xy=x^3+x^2-7x+5\)
112.a1	112a2	112.a	112a	$2$	$2$	\( 2^{4} \cdot 7 \)	\( 2^{11} \cdot 7^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$0.119959949$	$1$		$15$	$16$	$-0.234669$	$3543122/49$	$[0, 1, 0, -40, 84]$	\(y^2=x^3+x^2-40x+84\)
112.a2	112a1	112.a	112a	$2$	$2$	\( 2^{4} \cdot 7 \)	\( - 2^{10} \cdot 7 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$0.239919898$	$1$		$11$	$8$	$-0.581243$	$-4/7$	$[0, 1, 0, 0, 4]$	\(y^2=x^3+x^2+4\)
117.a1	117a4	117.a	117a	$4$	$4$	\( 3^{2} \cdot 13 \)	\( 3^{10} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$0.282583906$	$1$		$10$	$32$	$0.230940$	$37159393753/1053$	$[1, -1, 1, -626, 6180]$	\(y^2+xy+y=x^3-x^2-626x+6180\)
117.a2	117a3	117.a	117a	$4$	$4$	\( 3^{2} \cdot 13 \)	\( 3^{7} \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$0.282583906$	$1$		$10$	$32$	$0.230940$	$822656953/85683$	$[1, -1, 1, -176, -768]$	\(y^2+xy+y=x^3-x^2-176x-768\)
117.a3	117a2	117.a	117a	$4$	$4$	\( 3^{2} \cdot 13 \)	\( 3^{8} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$0.565167813$	$1$		$12$	$16$	$-0.115634$	$10218313/1521$	$[1, -1, 1, -41, 96]$	\(y^2+xy+y=x^3-x^2-41x+96\)
117.a4	117a1	117.a	117a	$4$	$4$	\( 3^{2} \cdot 13 \)	\( - 3^{7} \cdot 13 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1.130335626$	$1$		$11$	$8$	$-0.462207$	$12167/39$	$[1, -1, 1, 4, 6]$	\(y^2+xy+y=x^3-x^2+4x+6\)
118.a1	118a1	118.a	118a	$1$	$1$	\( 2 \cdot 59 \)	\( - 2^{2} \cdot 59 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.087906195$	$1$		$10$	$4$	$-0.864291$	$12167/236$	$[1, 1, 0, 1, 1]$	\(y^2+xy=x^3+x^2+x+1\)
121.b1	121b2	121.b	121b	$2$	$11$	\( 11^{2} \)	\( - 11^{9} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-11})$	$-11$	$N(\mathrm{U}(1))$		✓	$11$	11.120.1.10	11B.1.8	$0.987636717$	$1$		$4$	$44$	$0.575875$	$-32768$	$[0, -1, 1, -887, -10143]$	\(y^2+y=x^3-x^2-887x-10143\)
121.b2	121b1	121.b	121b	$2$	$11$	\( 11^{2} \)	\( - 11^{3} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-11})$	$-11$	$N(\mathrm{U}(1))$		✓	$11$	11.120.1.5	11B.1.3	$0.089785156$	$1$		$6$	$4$	$-0.623073$	$-32768$	$[0, -1, 1, -7, 10]$	\(y^2+y=x^3-x^2-7x+10\)
122.a1	122a1	122.a	122a	$1$	$1$	\( 2 \cdot 61 \)	\( - 2^{4} \cdot 61 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.120843215$	$1$		$10$	$8$	$-0.736916$	$1685159/976$	$[1, 0, 1, 2, 0]$	\(y^2+xy+y=x^3+2x\)
123.a1	123a1	123.a	123a	$2$	$5$	\( 3 \cdot 41 \)	\( - 3^{5} \cdot 41 \)	$1$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.1	5B.1.1	$0.840521417$	$1$		$14$	$20$	$-0.486743$	$-122023936/9963$	$[0, 1, 1, -10, 10]$	\(y^2+y=x^3+x^2-10x+10\)
123.a2	123a2	123.a	123a	$2$	$5$	\( 3 \cdot 41 \)	\( - 3 \cdot 41^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.3	5B.1.2	$0.168104283$	$1$		$4$	$100$	$0.317976$	$841232384/347568603$	$[0, 1, 1, 20, -890]$	\(y^2+y=x^3+x^2+20x-890\)
123.b1	123b1	123.b	123b	$1$	$1$	\( 3 \cdot 41 \)	\( - 3 \cdot 41 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.291914528$	$1$		$6$	$4$	$-0.916160$	$32768/123$	$[0, -1, 1, 1, -1]$	\(y^2+y=x^3-x^2+x-1\)
124.a1	124a1	124.a	124a	$2$	$3$	\( 2^{2} \cdot 31 \)	\( - 2^{4} \cdot 31 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$0.520530693$	$1$		$10$	$6$	$-0.771762$	$-87808/31$	$[0, 1, 0, -2, 1]$	\(y^2=x^3+x^2-2x+1\)
124.a2	124a2	124.a	124a	$2$	$3$	\( 2^{2} \cdot 31 \)	\( - 2^{4} \cdot 31^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$0.173510231$	$1$		$6$	$18$	$-0.222456$	$38112512/29791$	$[0, 1, 0, 18, -11]$	\(y^2=x^3+x^2+18x-11\)
128.a1	128a2	128.a	128a	$2$	$2$	\( 2^{7} \)	\( 2^{13} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.96.0.104	2B	$0.216165582$	$1$		$11$	$8$	$-0.509856$	$10976$	$[0, 1, 0, -9, 7]$	\(y^2=x^3+x^2-9x+7\)
128.a2	128a1	128.a	128a	$2$	$2$	\( 2^{7} \)	\( - 2^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.96.0.27	2B	$0.432331164$	$1$		$7$	$4$	$-0.856430$	$128$	$[0, 1, 0, 1, 1]$	\(y^2=x^3+x^2+x+1\)
129.a1	129a1	129.a	129a	$1$	$1$	\( 3 \cdot 43 \)	\( - 3^{4} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.099959152$	$1$		$8$	$8$	$-0.467113$	$-799178752/3483$	$[0, -1, 1, -19, 39]$	\(y^2+y=x^3-x^2-19x+39\)
130.a1	130a3	130.a	130a	$4$	$6$	\( 2 \cdot 5 \cdot 13 \)	\( 2^{12} \cdot 5 \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.21, 3.8.0.2	2B, 3B.1.2	$0.390154717$	$1$		$7$	$72$	$0.230449$	$988345570681/44994560$	$[1, 0, 1, -208, -1122]$	\(y^2+xy+y=x^3-208x-1122\)
130.a2	130a1	130.a	130a	$4$	$6$	\( 2 \cdot 5 \cdot 13 \)	\( 2^{4} \cdot 5^{3} \cdot 13 \)	$1$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.21, 3.8.0.1	2B, 3B.1.1	$1.170464153$	$1$		$13$	$24$	$-0.318857$	$3803721481/26000$	$[1, 0, 1, -33, 68]$	\(y^2+xy+y=x^3-33x+68\)
130.a3	130a2	130.a	130a	$4$	$6$	\( 2 \cdot 5 \cdot 13 \)	\( - 2^{2} \cdot 5^{6} \cdot 13^{2} \)	$1$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	4.12.0.12, 3.8.0.1	2B, 3B.1.1	$0.585232076$	$1$		$20$	$48$	$0.027717$	$-217081801/10562500$	$[1, 0, 1, -13, 156]$	\(y^2+xy+y=x^3-13x+156\)
130.a4	130a4	130.a	130a	$4$	$6$	\( 2 \cdot 5 \cdot 13 \)	\( - 2^{6} \cdot 5^{2} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	4.12.0.12, 3.8.0.2	2B, 3B.1.2	$0.195077358$	$1$		$14$	$144$	$0.577023$	$157376536199/7722894400$	$[1, 0, 1, 112, -4194]$	\(y^2+xy+y=x^3+112x-4194\)
131.a1	131a1	131.a	131a	$1$	$1$	\( 131 \)	\( -131 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.216095198$	$1$		$4$	$2$	$-0.911046$	$32768/131$	$[0, -1, 1, 1, 0]$	\(y^2+y=x^3-x^2+x\)
135.a1	135a1	135.a	135a	$1$	$1$	\( 3^{3} \cdot 5 \)	\( - 3^{5} \cdot 5^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.029545685$	$1$		$14$	$12$	$-0.584727$	$-12288/25$	$[0, 0, 1, -3, 4]$	\(y^2+y=x^3-3x+4\)

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