Elliptic curve search results

Results (1-50 of 4811 matches)

 

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
100.a1	100a3	100.a	100a	$4$	$6$	\( 2^{2} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.24, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$36$	$0.424075$	$488095744/125$	$[0, -1, 0, -1033, -12438]$	\(y^2=x^3-x^2-1033x-12438\)
100.a2	100a4	100.a	100a	$4$	$6$	\( 2^{2} \cdot 5^{2} \)	\( - 2^{8} \cdot 5^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.38, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$72$	$0.770649$	$-20720464/15625$	$[0, -1, 0, -908, -15688]$	\(y^2=x^3-x^2-908x-15688\)
100.a3	100a1	100.a	100a	$4$	$6$	\( 2^{2} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.24, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$12$	$-0.125231$	$16384/5$	$[0, -1, 0, -33, 62]$	\(y^2=x^3-x^2-33x+62\)
100.a4	100a2	100.a	100a	$4$	$6$	\( 2^{2} \cdot 5^{2} \)	\( - 2^{8} \cdot 5^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.38, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$24$	$0.221343$	$21296/25$	$[0, -1, 0, 92, 312]$	\(y^2=x^3-x^2+92x+312\)
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	$0.286507785$	$1$		$8$	$16$	$-0.416955$	$46268279/46818$	$[1, 1, 0, 8, 10]$	\(y^2+xy=x^3+x^2+8x+10\)
102.b1	102c3	102.b	102c	$4$	$6$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{18} \cdot 3^{2} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.4, 3.8.0.2	2B, 3B.1.2	$1$	$1$		$1$	$72$	$0.641426$	$46753267515625/11591221248$	$[1, 0, 1, -751, -6046]$	\(y^2+xy+y=x^3-751x-6046\)
102.b2	102c1	102.b	102c	$4$	$6$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{6} \cdot 3^{6} \cdot 17 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.4, 3.8.0.1	2B, 3B.1.1	$1$	$1$		$5$	$24$	$0.092120$	$1845026709625/793152$	$[1, 0, 1, -256, 1550]$	\(y^2+xy+y=x^3-256x+1550\)
102.b3	102c2	102.b	102c	$4$	$6$	\( 2 \cdot 3 \cdot 17 \)	\( - 2^{3} \cdot 3^{12} \cdot 17^{2} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.5, 3.8.0.1	2B, 3B.1.1	$1$	$1$		$4$	$48$	$0.438694$	$-1107111813625/1228691592$	$[1, 0, 1, -216, 2062]$	\(y^2+xy+y=x^3-216x+2062\)
102.b4	102c4	102.b	102c	$4$	$6$	\( 2 \cdot 3 \cdot 17 \)	\( - 2^{9} \cdot 3^{4} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.5, 3.8.0.2	2B, 3B.1.2	$1$	$1$		$0$	$144$	$0.988000$	$655215969476375/1001033261568$	$[1, 0, 1, 1809, -37790]$	\(y^2+xy+y=x^3+1809x-37790\)
102.c1	102b5	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( 2 \cdot 3^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.136	2B	$1$	$4$	$2$	$0$	$128$	$0.847078$	$2361739090258884097/5202$	$[1, 0, 0, -27744, -1781010]$	\(y^2+xy=x^3-27744x-1781010\)
102.c2	102b3	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{2} \cdot 3^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.48	2Cs	$1$	$1$		$2$	$64$	$0.500504$	$576615941610337/27060804$	$[1, 0, 0, -1734, -27936]$	\(y^2+xy=x^3-1734x-27936\)
102.c3	102b6	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( - 2 \cdot 3^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.165	2B	$1$	$1$		$0$	$128$	$0.847078$	$-491411892194497/125563633938$	$[1, 0, 0, -1644, -30942]$	\(y^2+xy=x^3-1644x-30942\)
102.c4	102b2	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{4} \cdot 3^{8} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.38	2Cs	$1$	$1$		$6$	$32$	$0.153931$	$163936758817/30338064$	$[1, 0, 0, -114, -396]$	\(y^2+xy=x^3-114x-396\)
102.c5	102b1	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{8} \cdot 3^{4} \cdot 17 \)	$0$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.97	2B	$1$	$1$		$7$	$16$	$-0.192642$	$4354703137/352512$	$[1, 0, 0, -34, 68]$	\(y^2+xy=x^3-34x+68\)
102.c6	102b4	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( - 2^{2} \cdot 3^{16} \cdot 17 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.99	2B	$1$	$1$		$2$	$64$	$0.500504$	$1276229915423/2927177028$	$[1, 0, 0, 226, -2232]$	\(y^2+xy=x^3+226x-2232\)
104.a1	104a1	104.a	104a	$1$	$1$	\( 2^{3} \cdot 13 \)	\( - 2^{11} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$8$	$-0.393032$	$-235298/13$	$[0, 1, 0, -16, -32]$	\(y^2=x^3+x^2-16x-32\)
105.a1	105a3	105.a	105a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \)	\( 3 \cdot 5^{4} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$1$	$1$		$0$	$16$	$-0.165962$	$157551496201/13125$	$[1, 0, 1, -113, -469]$	\(y^2+xy+y=x^3-113x-469\)
105.a2	105a2	105.a	105a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$1$	$1$		$2$	$8$	$-0.512536$	$47045881/11025$	$[1, 0, 1, -8, -7]$	\(y^2+xy+y=x^3-8x-7\)
105.a3	105a1	105.a	105a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \)	\( 3 \cdot 5 \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$1$	$1$		$1$	$4$	$-0.859109$	$1771561/105$	$[1, 0, 1, -3, 1]$	\(y^2+xy+y=x^3-3x+1\)
105.a4	105a4	105.a	105a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \)	\( - 3^{4} \cdot 5 \cdot 7^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$1$	$1$		$2$	$16$	$-0.165962$	$590589719/972405$	$[1, 0, 1, 17, -37]$	\(y^2+xy+y=x^3+17x-37\)
106.a1	106b1	106.a	106b	$1$	$1$	\( 2 \cdot 53 \)	\( - 2^{4} \cdot 53 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.068912680$	$1$		$10$	$8$	$-0.641726$	$-47045881/848$	$[1, 1, 0, -7, 5]$	\(y^2+xy=x^3+x^2-7x+5\)
106.b1	106d1	106.b	106d	$1$	$1$	\( 2 \cdot 53 \)	\( - 2^{5} \cdot 53 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$10$	$-0.446259$	$-2305199161/1696$	$[1, 1, 0, -27, -67]$	\(y^2+xy=x^3+x^2-27x-67\)
106.c1	106a2	106.c	106a	$2$	$3$	\( 2 \cdot 53 \)	\( - 2 \cdot 53^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$1$	$1$		$0$	$18$	$-0.263907$	$-81182737/297754$	$[1, 0, 0, -9, -29]$	\(y^2+xy=x^3-9x-29\)
106.c2	106a1	106.c	106a	$2$	$3$	\( 2 \cdot 53 \)	\( - 2^{3} \cdot 53 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$1$	$1$		$2$	$6$	$-0.813213$	$103823/424$	$[1, 0, 0, 1, 1]$	\(y^2+xy=x^3+x+1\)
106.d1	106c2	106.d	106c	$2$	$3$	\( 2 \cdot 53 \)	\( - 2^{8} \cdot 53^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$1$	$1$		$0$	$144$	$0.977397$	$-1646982616152408625/38112512$	$[1, 0, 0, -24603, -1487407]$	\(y^2+xy=x^3-24603x-1487407\)
106.d2	106c1	106.d	106c	$2$	$3$	\( 2 \cdot 53 \)	\( - 2^{24} \cdot 53 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$1$	$1$		$2$	$48$	$0.428091$	$-2507141976625/889192448$	$[1, 0, 0, -283, -2351]$	\(y^2+xy=x^3-283x-2351\)
108.a1	108a2	108.a	108a	$2$	$3$	\( 2^{2} \cdot 3^{3} \)	\( - 2^{8} \cdot 3^{9} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.648.18.4	3B.1.2	$1$	$1$		$0$	$18$	$-0.035060$	$0$	$[0, 0, 0, 0, -108]$	\(y^2=x^3-108\)
108.a2	108a1	108.a	108a	$2$	$3$	\( 2^{2} \cdot 3^{3} \)	\( - 2^{8} \cdot 3^{3} \)	$0$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.648.18.1	3B.1.1	$1$	$1$		$2$	$6$	$-0.584366$	$0$	$[0, 0, 0, 0, 4]$	\(y^2=x^3+4\)
109.a1	109a1	109.a	109a	$1$	$1$	\( 109 \)	\( -109 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$4$	$-0.716676$	$-60698457/109$	$[1, -1, 0, -8, -7]$	\(y^2+xy=x^3-x^2-8x-7\)
110.a1	110c1	110.a	110c	$2$	$3$	\( 2 \cdot 5 \cdot 11 \)	\( - 2^{7} \cdot 5 \cdot 11^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$1$	$1$		$2$	$28$	$-0.047191$	$-76711450249/851840$	$[1, 0, 1, -89, 316]$	\(y^2+xy+y=x^3-89x+316\)
110.a2	110c2	110.a	110c	$2$	$3$	\( 2 \cdot 5 \cdot 11 \)	\( - 2^{21} \cdot 5^{3} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$1$	$1$		$0$	$84$	$0.502115$	$2882081488391/2883584000$	$[1, 0, 1, 296, 1702]$	\(y^2+xy+y=x^3+296x+1702\)
110.b1	110a2	110.b	110a	$2$	$5$	\( 2 \cdot 5 \cdot 11 \)	\( - 2 \cdot 5 \cdot 11^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.3	5B.1.2	$1$	$1$		$0$	$100$	$0.645076$	$-23178622194826561/1610510$	$[1, 1, 1, -5940, -178685]$	\(y^2+xy+y=x^3+x^2-5940x-178685\)
110.b2	110a1	110.b	110a	$2$	$5$	\( 2 \cdot 5 \cdot 11 \)	\( - 2^{5} \cdot 5^{5} \cdot 11 \)	$0$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.1	5B.1.1	$1$	$1$		$4$	$20$	$-0.159643$	$109902239/1100000$	$[1, 1, 1, 10, -45]$	\(y^2+xy+y=x^3+x^2+10x-45\)
110.c1	110b1	110.c	110b	$2$	$3$	\( 2 \cdot 5 \cdot 11 \)	\( - 2^{3} \cdot 5 \cdot 11 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$1$	$1$		$2$	$4$	$-0.807105$	$-117649/440$	$[1, 0, 0, -1, 1]$	\(y^2+xy=x^3-x+1\)
110.c2	110b2	110.c	110b	$2$	$3$	\( 2 \cdot 5 \cdot 11 \)	\( - 2 \cdot 5^{3} \cdot 11^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$1$	$1$		$0$	$12$	$-0.257799$	$80062991/332750$	$[1, 0, 0, 9, -25]$	\(y^2+xy=x^3+9x-25\)
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	$0.239919898$	$1$		$11$	$8$	$-0.581243$	$-4/7$	$[0, 1, 0, 0, 4]$	\(y^2=x^3+x^2+4\)
112.b1	112b3	112.b	112b	$4$	$4$	\( 2^{4} \cdot 7 \)	\( 2^{11} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.101	2B	$1$	$1$		$1$	$16$	$-0.002033$	$1443468546/7$	$[0, 0, 0, -299, -1990]$	\(y^2=x^3-299x-1990\)
112.b2	112b4	112.b	112b	$4$	$4$	\( 2^{4} \cdot 7 \)	\( 2^{11} \cdot 7^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.49	2B	$1$	$1$		$3$	$16$	$-0.002033$	$11090466/2401$	$[0, 0, 0, -59, 138]$	\(y^2=x^3-59x+138\)
112.b3	112b2	112.b	112b	$4$	$4$	\( 2^{4} \cdot 7 \)	\( 2^{10} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.2	2Cs	$1$	$1$		$3$	$8$	$-0.348607$	$740772/49$	$[0, 0, 0, -19, -30]$	\(y^2=x^3-19x-30\)
112.b4	112b1	112.b	112b	$4$	$4$	\( 2^{4} \cdot 7 \)	\( - 2^{8} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.60	2B	$1$	$1$		$1$	$4$	$-0.695180$	$432/7$	$[0, 0, 0, 1, -2]$	\(y^2=x^3+x-2\)
112.c1	112c6	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( 2^{21} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$1$	$1$		$1$	$144$	$1.106249$	$2251439055699625/25088$	$[0, -1, 0, -43688, 3529328]$	\(y^2=x^3-x^2-43688x+3529328\)
112.c2	112c5	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( - 2^{30} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$1$	$1$		$1$	$72$	$0.759675$	$-548347731625/1835008$	$[0, -1, 0, -2728, 55920]$	\(y^2=x^3-x^2-2728x+55920\)
112.c3	112c4	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( 2^{15} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.12.0.1	2B, 3Cs	$1$	$1$		$1$	$48$	$0.556942$	$4956477625/941192$	$[0, -1, 0, -568, 4464]$	\(y^2=x^3-x^2-568x+4464\)
112.c4	112c2	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( 2^{13} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$1$	$1$		$1$	$16$	$0.007636$	$128787625/98$	$[0, -1, 0, -168, -784]$	\(y^2=x^3-x^2-168x-784\)
112.c5	112c1	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( - 2^{14} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$1$	$1$		$1$	$8$	$-0.338938$	$-15625/28$	$[0, -1, 0, -8, -16]$	\(y^2=x^3-x^2-8x-16\)
112.c6	112c3	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( - 2^{18} \cdot 7^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.12.0.1	2B, 3Cs	$1$	$1$		$1$	$24$	$0.210368$	$9938375/21952$	$[0, -1, 0, 72, 368]$	\(y^2=x^3-x^2+72x+368\)
113.a1	113a2	113.a	113a	$2$	$2$	\( 113 \)	\( 113 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.22	2B	$1$	$1$		$1$	$12$	$-0.876173$	$912673/113$	$[1, 1, 1, -2, -2]$	\(y^2+xy+y=x^3+x^2-2x-2\)