Elliptic curve search results

Results (18 matches)

  Download displayed columns for results to

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	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
8330.r2	8330z1	8330.r	8330z	$2$	$3$	\( 2 \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{12} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$0.239821889$	$1$		$6$	$2304$	$0.204185$	$375078431/1740800$	$1.00008$	$2.83388$	$[1, 1, 1, 55, -393]$	\(y^2+xy+y=x^3+x^2+55x-393\)	3.4.0.a.1, 21.8.0-3.a.1.1, 68.2.0.a.1, 204.8.0.?, 1428.16.0.?	$[(7, 16)]$
8330.x2	8330n1	8330.x	8330n	$2$	$3$	\( 2 \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{12} \cdot 5^{2} \cdot 7^{8} \cdot 17 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$204$	$16$	$0$	$1$	$1$		$2$	$16128$	$1.177141$	$375078431/1740800$	$1.00008$	$4.12719$	$[1, 0, 0, 2694, 142820]$	\(y^2+xy=x^3+2694x+142820\)	3.8.0-3.a.1.2, 68.2.0.a.1, 204.16.0.?	$[ ]$
41650.k2	41650e1	41650.k	41650e	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{12} \cdot 5^{8} \cdot 7^{8} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1020$	$16$	$0$	$1$	$1$		$0$	$387072$	$1.981859$	$375078431/1740800$	$1.00008$	$4.41055$	$[1, 1, 0, 67350, 17852500]$	\(y^2+xy=x^3+x^2+67350x+17852500\)	3.4.0.a.1, 15.8.0-3.a.1.2, 68.2.0.a.1, 204.8.0.?, 1020.16.0.?	$[ ]$
41650.z2	41650h1	41650.z	41650h	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{12} \cdot 5^{8} \cdot 7^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$7140$	$16$	$0$	$1$	$1$		$0$	$55296$	$1.008904$	$375078431/1740800$	$1.00008$	$3.31293$	$[1, 0, 1, 1374, -51852]$	\(y^2+xy+y=x^3+1374x-51852\)	3.4.0.a.1, 68.2.0.a.1, 105.8.0.?, 204.8.0.?, 7140.16.0.?	$[ ]$
66640.i2	66640w1	66640.i	66640w	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{24} \cdot 5^{2} \cdot 7^{8} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$204$	$16$	$0$	$1$	$1$		$0$	$387072$	$1.870287$	$375078431/1740800$	$1.00008$	$4.10338$	$[0, -1, 0, 43104, -9140480]$	\(y^2=x^3-x^2+43104x-9140480\)	3.4.0.a.1, 12.8.0-3.a.1.1, 68.2.0.a.1, 102.8.0.?, 204.16.0.?	$[ ]$
66640.cb2	66640cn1	66640.cb	66640cn	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{24} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$2.526162680$	$1$		$2$	$55296$	$0.897332$	$375078431/1740800$	$1.00008$	$3.05220$	$[0, 1, 0, 880, 26900]$	\(y^2=x^3+x^2+880x+26900\)	3.4.0.a.1, 68.2.0.a.1, 84.8.0.?, 204.8.0.?, 714.8.0.?, $\ldots$	$[(20, 230)]$
74970.d2	74970u1	74970.d	74970u	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{6} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$0.886526346$	$1$		$4$	$69120$	$0.753491$	$375078431/1740800$	$1.00008$	$2.86640$	$[1, -1, 0, 495, 11101]$	\(y^2+xy=x^3-x^2+495x+11101\)	3.4.0.a.1, 21.8.0-3.a.1.2, 68.2.0.a.1, 204.8.0.?, 1428.16.0.?	$[(18, 151)]$
74970.bh2	74970bm1	74970.bh	74970bm	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{6} \cdot 5^{2} \cdot 7^{8} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$204$	$16$	$0$	$1$	$1$		$0$	$483840$	$1.726446$	$375078431/1740800$	$1.00008$	$3.90654$	$[1, -1, 0, 24246, -3856140]$	\(y^2+xy=x^3-x^2+24246x-3856140\)	3.8.0-3.a.1.1, 68.2.0.a.1, 204.16.0.?	$[ ]$
141610.cc2	141610n1	141610.cc	141610n	$2$	$3$	\( 2 \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{12} \cdot 5^{2} \cdot 7^{8} \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$204$	$16$	$0$	$1.581319114$	$1$		$4$	$4644864$	$2.593746$	$375078431/1740800$	$1.00008$	$4.57455$	$[1, 1, 1, 778560, 700896097]$	\(y^2+xy+y=x^3+x^2+778560x+700896097\)	3.4.0.a.1, 12.8.0-3.a.1.3, 51.8.0-3.a.1.2, 68.2.0.a.1, 204.16.0.?	$[(-203, 23221)]$
141610.ck2	141610y1	141610.ck	141610y	$2$	$3$	\( 2 \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{12} \cdot 5^{2} \cdot 7^{2} \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1428$	$16$	$0$	$0.421359291$	$1$		$4$	$663552$	$1.620792$	$375078431/1740800$	$1.00008$	$3.59018$	$[1, 0, 0, 15889, -2041159]$	\(y^2+xy=x^3+15889x-2041159\)	3.4.0.a.1, 68.2.0.a.1, 84.8.0.?, 204.8.0.?, 357.8.0.?, $\ldots$	$[(806, 22717)]$
266560.bv2	266560bv1	266560.bv	266560bv	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{30} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2856$	$16$	$0$	$1$	$1$		$0$	$442368$	$1.243906$	$375078431/1740800$	$1.00008$	$3.04641$	$[0, -1, 0, 3519, 211681]$	\(y^2=x^3-x^2+3519x+211681\)	3.4.0.a.1, 68.2.0.a.1, 168.8.0.?, 204.8.0.?, 2856.16.0.?	$[ ]$
266560.cb2	266560cb1	266560.cb	266560cb	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{30} \cdot 5^{2} \cdot 7^{8} \cdot 17 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$408$	$16$	$0$	$2.599648101$	$1$		$8$	$3096576$	$2.216862$	$375078431/1740800$	$1.00008$	$3.98094$	$[0, -1, 0, 172415, 72951425]$	\(y^2=x^3-x^2+172415x+72951425\)	3.4.0.a.1, 24.8.0-3.a.1.2, 68.2.0.a.1, 204.8.0.?, 408.16.0.?	$[(6305, 501760), (-65, 7840)]$
266560.fe2	266560fe1	266560.fe	266560fe	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{30} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2856$	$16$	$0$	$2.917788381$	$1$		$2$	$442368$	$1.243906$	$375078431/1740800$	$1.00008$	$3.04641$	$[0, 1, 0, 3519, -211681]$	\(y^2=x^3+x^2+3519x-211681\)	3.4.0.a.1, 68.2.0.a.1, 168.8.0.?, 204.8.0.?, 2856.16.0.?	$[(1147, 38912)]$
266560.gh2	266560gh1	266560.gh	266560gh	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{30} \cdot 5^{2} \cdot 7^{8} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$408$	$16$	$0$	$17.59931745$	$1$		$0$	$3096576$	$2.216862$	$375078431/1740800$	$1.00008$	$3.98094$	$[0, 1, 0, 172415, -72951425]$	\(y^2=x^3+x^2+172415x-72951425\)	3.4.0.a.1, 24.8.0-3.a.1.4, 68.2.0.a.1, 204.8.0.?, 408.16.0.?	$[(89311305/547, 373103256560/547)]$
333200.bt2	333200bt1	333200.bt	333200bt	$2$	$3$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{24} \cdot 5^{8} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$7140$	$16$	$0$	$5.412144109$	$1$		$0$	$1327104$	$1.702051$	$375078431/1740800$	$1.00008$	$3.42528$	$[0, -1, 0, 21992, 3318512]$	\(y^2=x^3-x^2+21992x+3318512\)	3.4.0.a.1, 68.2.0.a.1, 204.8.0.?, 420.8.0.?, 3570.8.0.?, $\ldots$	$[(298/3, 54550/3)]$
333200.ew2	333200ew1	333200.ew	333200ew	$2$	$3$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{24} \cdot 5^{8} \cdot 7^{8} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1020$	$16$	$0$	$5.737865288$	$1$		$2$	$9289728$	$2.675007$	$375078431/1740800$	$1.00008$	$4.34342$	$[0, 1, 0, 1077592, -1140404812]$	\(y^2=x^3+x^2+1077592x-1140404812\)	3.4.0.a.1, 60.8.0-3.a.1.2, 68.2.0.a.1, 204.8.0.?, 510.8.0.?, $\ldots$	$[(2348, 119750)]$
374850.jg2	374850jg1	374850.jg	374850jg	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{6} \cdot 5^{8} \cdot 7^{8} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1020$	$16$	$0$	$4.864245133$	$1$		$2$	$11612160$	$2.531166$	$375078431/1740800$	$1.00008$	$4.16907$	$[1, -1, 1, 606145, -481411353]$	\(y^2+xy+y=x^3-x^2+606145x-481411353\)	3.4.0.a.1, 15.8.0-3.a.1.1, 68.2.0.a.1, 204.8.0.?, 1020.16.0.?	$[(549, 3800)]$
374850.jy2	374850jy1	374850.jy	374850jy	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{6} \cdot 5^{8} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$7140$	$16$	$0$	$1.524286967$	$1$		$4$	$1658880$	$1.558210$	$375078431/1740800$	$1.00008$	$3.25936$	$[1, -1, 1, 12370, 1399997]$	\(y^2+xy+y=x^3-x^2+12370x+1399997\)	3.4.0.a.1, 68.2.0.a.1, 105.8.0.?, 204.8.0.?, 7140.16.0.?	$[(-71, 435)]$

  Download displayed columns for results to