Elliptic curve search results

Results (27 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	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
2310.c3	2310c1	2310.c	2310c	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.12	2B	$264$	$48$	$0$	$1.096677767$	$1$		$7$	$1536$	$0.457659$	$71210194441849/165580800$	$0.92929$	$4.11835$	$[1, 1, 0, -863, -10107]$	\(y^2+xy=x^3+x^2-863x-10107\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.2, 24.24.0-24.bb.1.2, $\ldots$	$[(-17, 5)]$
6930.bf3	6930bi1	6930.bf	6930bi	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$264$	$48$	$0$	$0.506442628$	$1$		$17$	$12288$	$1.006966$	$71210194441849/165580800$	$0.92929$	$4.35210$	$[1, -1, 1, -7772, 265119]$	\(y^2+xy+y=x^3-x^2-7772x+265119\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.bb.1.4, 66.6.0.a.1, 88.24.0.?, $\ldots$	$[(57, 41)]$
11550.cl3	11550ci1	11550.cl	11550ci	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1$	$1$		$1$	$36864$	$1.262377$	$71210194441849/165580800$	$0.92929$	$4.44209$	$[1, 0, 0, -21588, -1220208]$	\(y^2+xy=x^3-21588x-1220208\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 40.12.0-4.c.1.4, 60.12.0-4.c.1.2, $\ldots$	$[]$
16170.bh3	16170bf1	16170.bh	16170bf	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$3.639206893$	$1$		$3$	$73728$	$1.430614$	$71210194441849/165580800$	$0.92929$	$4.49618$	$[1, 0, 1, -42313, 3339788]$	\(y^2+xy+y=x^3-42313x+3339788\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 56.12.0-4.c.1.4, 66.6.0.a.1, $\ldots$	$[(699, 17410)]$
18480.bt3	18480cn1	18480.bt	18480cn	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$264$	$48$	$0$	$1.453660662$	$1$		$3$	$36864$	$1.150806$	$71210194441849/165580800$	$0.92929$	$4.09330$	$[0, 1, 0, -13816, 619220]$	\(y^2=x^3+x^2-13816x+619220\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.1, 24.24.0-24.bb.1.10, $\ldots$	$[(52, 210)]$
25410.bn3	25410bm1	25410.bn	25410bm	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{12} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$264$	$48$	$0$	$0.957375168$	$1$		$13$	$184320$	$1.656607$	$71210194441849/165580800$	$0.92929$	$4.56320$	$[1, 1, 1, -104486, 12930083]$	\(y^2+xy+y=x^3+x^2-104486x+12930083\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.bb.1.13, 66.6.0.a.1, 88.24.0.?, $\ldots$	$[(161, 479)]$
34650.h3	34650m1	34650.h	34650m	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1$	$1$		$1$	$294912$	$1.811684$	$71210194441849/165580800$	$0.92929$	$4.60583$	$[1, -1, 0, -194292, 32945616]$	\(y^2+xy=x^3-x^2-194292x+32945616\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.bb.1, 66.6.0.a.1, $\ldots$	$[]$
48510.cp3	48510da1	48510.cp	48510da	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3^{7} \cdot 5^{2} \cdot 7^{8} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$589824$	$1.979919$	$71210194441849/165580800$	$0.92929$	$4.64930$	$[1, -1, 1, -380813, -90174283]$	\(y^2+xy+y=x^3-x^2-380813x-90174283\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 28.12.0-4.c.1.2, 66.6.0.a.1, $\ldots$	$[]$
55440.dh3	55440ej1	55440.dh	55440ej	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{24} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$264$	$48$	$0$	$2.653673982$	$1$		$5$	$294912$	$1.700111$	$71210194441849/165580800$	$0.92929$	$4.28507$	$[0, 0, 0, -124347, -16843286]$	\(y^2=x^3-124347x-16843286\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.bb.1.12, 66.6.0.a.1, 88.24.0.?, $\ldots$	$[(-202, 180)]$
73920.de3	73920fo1	73920.de	73920fo	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{30} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$264$	$48$	$0$	$1$	$1$		$1$	$294912$	$1.497379$	$71210194441849/165580800$	$0.92929$	$3.95811$	$[0, -1, 0, -55265, 5009025]$	\(y^2=x^3-x^2-55265x+5009025\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 24.24.0-24.bb.1.6, 66.6.0.a.1, $\ldots$	$[]$
73920.hy3	73920do1	73920.hy	73920do	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{30} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$264$	$48$	$0$	$1$	$4$	$2$	$1$	$294912$	$1.497379$	$71210194441849/165580800$	$0.92929$	$3.95811$	$[0, 1, 0, -55265, -5009025]$	\(y^2=x^3+x^2-55265x-5009025\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 24.24.0-24.bb.1.14, 66.6.0.a.1, $\ldots$	$[]$
76230.bz3	76230by1	76230.bz	76230by	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{12} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.13	2B	$264$	$48$	$0$	$1$	$1$		$1$	$1474560$	$2.205914$	$71210194441849/165580800$	$0.92929$	$4.70361$	$[1, -1, 0, -940374, -350052620]$	\(y^2+xy=x^3-x^2-940374x-350052620\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.6, 12.12.0-4.c.1.2, 24.24.0-24.bb.1.15, $\ldots$	$[]$
80850.ei3	80850ev1	80850.ei	80850ev	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$1769472$	$2.235332$	$71210194441849/165580800$	$0.92929$	$4.71036$	$[1, 1, 1, -1057813, 417473531]$	\(y^2+xy+y=x^3+x^2-1057813x+417473531\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 66.6.0.a.1, 88.12.0.?, $\ldots$	$[]$
92400.cr3	92400eh1	92400.cr	92400eh	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{24} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$3.557840170$	$1$		$3$	$884736$	$1.955524$	$71210194441849/165580800$	$0.92929$	$4.36169$	$[0, -1, 0, -345408, 78093312]$	\(y^2=x^3-x^2-345408x+78093312\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 40.12.0-4.c.1.4, 60.12.0-4.c.1.1, $\ldots$	$[(577, 8400)]$
127050.dt3	127050dq1	127050.dt	127050dq	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{12} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$1$	$1$		$1$	$4423680$	$2.461327$	$71210194441849/165580800$	$0.92929$	$4.75996$	$[1, 0, 1, -2612151, 1621484698]$	\(y^2+xy+y=x^3-2612151x+1621484698\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.bb.1, 66.6.0.a.1, $\ldots$	$[]$
129360.cv3	129360fd1	129360.cv	129360fd	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$4$	$2$	$1$	$1769472$	$2.123760$	$71210194441849/165580800$	$0.92929$	$4.40852$	$[0, -1, 0, -677000, -213746448]$	\(y^2=x^3-x^2-677000x-213746448\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 56.12.0-4.c.1.4, 66.6.0.a.1, $\ldots$	$[]$
177870.hv3	177870b1	177870.hv	177870b	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( 2^{12} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$8847360$	$2.629562$	$71210194441849/165580800$	$0.92929$	$4.79448$	$[1, 0, 0, -5119815, -4450377975]$	\(y^2+xy=x^3-5119815x-4450377975\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 28.12.0-4.c.1.2, 66.6.0.a.1, $\ldots$	$[]$
203280.fj3	203280bn1	203280.fj	203280bn	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$264$	$48$	$0$	$9.044279156$	$1$		$1$	$4423680$	$2.349754$	$71210194441849/165580800$	$0.92929$	$4.46738$	$[0, 1, 0, -1671776, -830868876]$	\(y^2=x^3+x^2-1671776x-830868876\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.bb.1.5, 66.6.0.a.1, 88.24.0.?, $\ldots$	$[(-48015/8, 657111/8)]$
221760.bq3	221760fo1	221760.bq	221760fo	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{30} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$264$	$48$	$0$	$2.105337749$	$1$		$5$	$2359296$	$2.046684$	$71210194441849/165580800$	$0.92929$	$4.14035$	$[0, 0, 0, -497388, -134746288]$	\(y^2=x^3-497388x-134746288\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 24.24.0-24.bb.1.8, 66.6.0.a.1, $\ldots$	$[(-419, 315)]$
221760.gn3	221760kq1	221760.gn	221760kq	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{30} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$264$	$48$	$0$	$1$	$1$		$1$	$2359296$	$2.046684$	$71210194441849/165580800$	$0.92929$	$4.14035$	$[0, 0, 0, -497388, 134746288]$	\(y^2=x^3-497388x+134746288\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 24.24.0-24.bb.1.16, 66.6.0.a.1, $\ldots$	$[]$
242550.a3	242550a1	242550.a	242550a	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3^{7} \cdot 5^{8} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$4.647998901$	$1$		$5$	$14155776$	$2.784637$	$71210194441849/165580800$	$0.92929$	$4.82463$	$[1, -1, 0, -9520317, -11281305659]$	\(y^2+xy=x^3-x^2-9520317x-11281305659\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 66.6.0.a.1, 88.12.0.?, $\ldots$	$[(-1782, 5659)]$
277200.nw3	277200nw1	277200.nw	277200nw	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{24} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$5.757472664$	$1$		$3$	$7077888$	$2.504829$	$71210194441849/165580800$	$0.92929$	$4.50531$	$[0, 0, 0, -3108675, -2105410750]$	\(y^2=x^3-3108675x-2105410750\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0.bb.1, 66.6.0.a.1, $\ldots$	$[(3170, 141050)]$
369600.b3	369600b1	369600.b	369600b	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{30} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$5.543654308$	$1$		$3$	$7077888$	$2.302097$	$71210194441849/165580800$	$0.92929$	$4.21445$	$[0, -1, 0, -1381633, -623364863]$	\(y^2=x^3-x^2-1381633x-623364863\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 40.12.0-4.c.1.5, 66.6.0.a.1, $\ldots$	$[(15681, 1957888)]$
369600.uk3	369600uk1	369600.uk	369600uk	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{30} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$7.537000652$	$1$		$1$	$7077888$	$2.302097$	$71210194441849/165580800$	$0.92929$	$4.21445$	$[0, 1, 0, -1381633, 623364863]$	\(y^2=x^3+x^2-1381633x+623364863\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 40.12.0-4.c.1.5, 66.6.0.a.1, $\ldots$	$[(34333/6, 2849525/6)]$
381150.my3	381150my1	381150.my	381150my	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{12} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1320$	$48$	$0$	$3.256874895$	$1$		$5$	$35389440$	$3.010632$	$71210194441849/165580800$	$0.92929$	$4.86597$	$[1, -1, 1, -23509355, -43780086853]$	\(y^2+xy+y=x^3-x^2-23509355x-43780086853\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 40.12.0-4.c.1.6, 60.12.0-4.c.1.2, $\ldots$	$[(-2757, 9946)]$
388080.hn3	388080hn1	388080.hn	388080hn	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{24} \cdot 3^{7} \cdot 5^{2} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1848$	$48$	$0$	$2.850804554$	$1$		$5$	$14155776$	$2.673069$	$71210194441849/165580800$	$0.92929$	$4.54439$	$[0, 0, 0, -6093003, 5777247098]$	\(y^2=x^3-6093003x+5777247098\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 28.12.0-4.c.1.1, 66.6.0.a.1, $\ldots$	$[(-59, 78336)]$
390390.dj3	390390dj1	390390.dj	390390dj	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} \)	\( 2^{12} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$1.979186564$	$1$		$7$	$2949120$	$1.740133$	$71210194441849/165580800$	$0.92929$	$3.67275$	$[1, 1, 1, -145935, -21475563]$	\(y^2+xy+y=x^3+x^2-145935x-21475563\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.bb.1, 66.6.0.a.1, 88.12.0.?, $\ldots$	$[(-213, 66)]$