Elliptic curve search results

Results (26 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	Manin constant
3234.r1	3234q2	3234.r	3234q	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{7} \cdot 3^{12} \cdot 7^{9} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$4$	$2$	$0$	$75264$	$2.295082$	$46546832455691959/748268928$	$1.13125$	$6.91612$	$[1, 1, 1, -2570492, -1587302179]$	\(y^2+xy+y=x^3+x^2-2570492x-1587302179\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
3234.u1	3234v2	3234.u	3234v	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{7} \cdot 3^{12} \cdot 7^{3} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$0.136499555$	$1$		$16$	$10752$	$1.322124$	$46546832455691959/748268928$	$1.13125$	$5.47140$	$[1, 0, 0, -52459, 4620209]$	\(y^2+xy=x^3-52459x+4620209\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(134, -31)]$	$1$
9702.g1	9702s2	9702.g	9702s	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{7} \cdot 3^{18} \cdot 7^{9} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$7.001493170$	$1$		$2$	$602112$	$2.844387$	$46546832455691959/748268928$	$1.13125$	$6.80648$	$[1, -1, 0, -23134428, 42834024400]$	\(y^2+xy=x^3-x^2-23134428x+42834024400\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(3111, 29506)]$	$1$
9702.q1	9702q2	9702.q	9702q	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{7} \cdot 3^{18} \cdot 7^{3} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$10.12538341$	$1$		$0$	$86016$	$1.871431$	$46546832455691959/748268928$	$1.13125$	$5.53466$	$[1, -1, 0, -472131, -124745643]$	\(y^2+xy=x^3-x^2-472131x-124745643\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(23383/2, 3526087/2)]$	$1$
25872.e1	25872bp2	25872.e	25872bp	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{19} \cdot 3^{12} \cdot 7^{3} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$4.682682833$	$1$		$3$	$258048$	$2.015274$	$46546832455691959/748268928$	$1.13125$	$5.17027$	$[0, -1, 0, -839344, -295693376]$	\(y^2=x^3-x^2-839344x-295693376\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(2389, 106434)]$	$1$
25872.cq1	25872cn2	25872.cq	25872cn	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{19} \cdot 3^{12} \cdot 7^{9} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$1806336$	$2.988228$	$46546832455691959/748268928$	$1.13125$	$6.31933$	$[0, 1, 0, -41127872, 101505083700]$	\(y^2=x^3+x^2-41127872x+101505083700\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
35574.m1	35574m2	35574.m	35574m	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11^{2} \)	\( 2^{7} \cdot 3^{12} \cdot 7^{9} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$8.693744992$	$1$		$0$	$9031680$	$3.494030$	$46546832455691959/748268928$	$1.13125$	$6.70649$	$[1, 1, 0, -311029534, 2111144052340]$	\(y^2+xy=x^3+x^2-311029534x+2111144052340\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(1026739/10, 8842693/10)]$	$1$
35574.x1	35574bi2	35574.x	35574bi	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11^{2} \)	\( 2^{7} \cdot 3^{12} \cdot 7^{3} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$0$	$1290240$	$2.521072$	$46546832455691959/748268928$	$1.13125$	$5.59235$	$[1, 0, 1, -6347542, -6155845720]$	\(y^2+xy+y=x^3-6347542x-6155845720\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
77616.cb1	77616gr2	77616.cb	77616gr	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{19} \cdot 3^{18} \cdot 7^{9} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$38.98730040$	$1$		$1$	$14450688$	$3.537533$	$46546832455691959/748268928$	$1.13125$	$6.28817$	$[0, 0, 0, -370150851, -2741007410750]$	\(y^2=x^3-370150851x-2741007410750\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(152289136128735687/1297921, 57955259251293609008414066/1297921)]$	$1$
77616.fm1	77616gm2	77616.fm	77616gm	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{19} \cdot 3^{18} \cdot 7^{3} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$7.971079926$	$1$		$1$	$2064384$	$2.564579$	$46546832455691959/748268928$	$1.13125$	$5.25123$	$[0, 0, 0, -7554099, 7991275250]$	\(y^2=x^3-7554099x+7991275250\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(16087/3, 381410/3)]$	$1$
80850.bp1	80850u2	80850.bp	80850u	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{7} \cdot 3^{12} \cdot 5^{6} \cdot 7^{3} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$2.715225991$	$1$		$4$	$1376256$	$2.126842$	$46546832455691959/748268928$	$1.13125$	$4.76743$	$[1, 1, 0, -1311475, 577526125]$	\(y^2+xy=x^3+x^2-1311475x+577526125\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(615, 1705)]$	$1$
80850.cq1	80850cr2	80850.cq	80850cr	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{7} \cdot 3^{12} \cdot 5^{6} \cdot 7^{9} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$0$	$9633792$	$3.099800$	$46546832455691959/748268928$	$1.13125$	$5.80062$	$[1, 0, 1, -64262301, -198284247752]$	\(y^2+xy+y=x^3-64262301x-198284247752\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
103488.bd1	103488go2	103488.bd	103488go	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{25} \cdot 3^{12} \cdot 7^{9} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$4$	$2$	$1$	$14450688$	$3.334801$	$46546832455691959/748268928$	$1.13125$	$5.92083$	$[0, -1, 0, -164511489, 812205181089]$	\(y^2=x^3-x^2-164511489x+812205181089\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
103488.do1	103488w2	103488.do	103488w	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{25} \cdot 3^{12} \cdot 7^{3} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$4$	$2$	$1$	$2064384$	$2.361847$	$46546832455691959/748268928$	$1.13125$	$4.90972$	$[0, -1, 0, -3357377, 2368904385]$	\(y^2=x^3-x^2-3357377x+2368904385\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
103488.ff1	103488dj2	103488.ff	103488dj	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{25} \cdot 3^{12} \cdot 7^{9} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$12.98453475$	$1$		$1$	$14450688$	$3.334801$	$46546832455691959/748268928$	$1.13125$	$5.92083$	$[0, 1, 0, -164511489, -812205181089]$	\(y^2=x^3+x^2-164511489x-812205181089\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(10510314/13, 33282940419/13)]$	$1$
103488.ik1	103488iq2	103488.ik	103488iq	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{25} \cdot 3^{12} \cdot 7^{3} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$7.794049226$	$1$		$3$	$2064384$	$2.361847$	$46546832455691959/748268928$	$1.13125$	$4.90972$	$[0, 1, 0, -3357377, -2368904385]$	\(y^2=x^3+x^2-3357377x-2368904385\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(29221, 4985100)]$	$1$
106722.ep1	106722hh2	106722.ep	106722hh	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{7} \cdot 3^{18} \cdot 7^{9} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$14.62979291$	$1$		$0$	$72253440$	$4.043335$	$46546832455691959/748268928$	$1.13125$	$6.63945$	$[1, -1, 1, -2799265811, -57003688678989]$	\(y^2+xy+y=x^3-x^2-2799265811x-57003688678989\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(33956697/19, 154868923296/19)]$	$1$
106722.he1	106722gy2	106722.he	106722gy	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{7} \cdot 3^{18} \cdot 7^{3} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$3.021672355$	$1$		$4$	$10321920$	$3.070377$	$46546832455691959/748268928$	$1.13125$	$5.63103$	$[1, -1, 1, -57127874, 166207834433]$	\(y^2+xy+y=x^3-x^2-57127874x+166207834433\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(4381, -981)]$	$1$
242550.ip1	242550ip2	242550.ip	242550ip	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{7} \cdot 3^{18} \cdot 5^{6} \cdot 7^{9} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$0$	$77070336$	$3.649105$	$46546832455691959/748268928$	$1.13125$	$5.81829$	$[1, -1, 1, -578360705, 5353674689297]$	\(y^2+xy+y=x^3-x^2-578360705x+5353674689297\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
242550.kn1	242550kn2	242550.kn	242550kn	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{7} \cdot 3^{18} \cdot 5^{6} \cdot 7^{3} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$0$	$11010048$	$2.676151$	$46546832455691959/748268928$	$1.13125$	$4.87664$	$[1, -1, 1, -11803280, -15605008653]$	\(y^2+xy+y=x^3-x^2-11803280x-15605008653\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
284592.bv1	284592bv2	284592.bv	284592bv	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 11^{2} \)	\( 2^{19} \cdot 3^{12} \cdot 7^{3} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$4$	$2$	$1$	$30965760$	$3.214222$	$46546832455691959/748268928$	$1.13125$	$5.32870$	$[0, -1, 0, -101560664, 393974126064]$	\(y^2=x^3-x^2-101560664x+393974126064\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
284592.jm1	284592jm2	284592.jm	284592jm	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 11^{2} \)	\( 2^{19} \cdot 3^{12} \cdot 7^{9} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$24.76668533$	$1$		$1$	$216760320$	$4.187172$	$46546832455691959/748268928$	$1.13125$	$6.25836$	$[0, 1, 0, -4976472552, -135123172294860]$	\(y^2=x^3+x^2-4976472552x-135123172294860\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(6773363748516/5089, 16905559134149637930/5089)]$	$1$
310464.dq1	310464dq2	310464.dq	310464dq	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{25} \cdot 3^{18} \cdot 7^{3} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$16515072$	$2.911152$	$46546832455691959/748268928$	$1.13125$	$5.00444$	$[0, 0, 0, -30216396, 63930202000]$	\(y^2=x^3-30216396x+63930202000\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
310464.fj1	310464fj2	310464.fj	310464fj	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{25} \cdot 3^{18} \cdot 7^{3} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$4$	$2$	$1$	$16515072$	$2.911152$	$46546832455691959/748268928$	$1.13125$	$5.00444$	$[0, 0, 0, -30216396, -63930202000]$	\(y^2=x^3-30216396x-63930202000\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
310464.mr1	310464mr2	310464.mr	310464mr	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{25} \cdot 3^{18} \cdot 7^{9} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$115605504$	$3.884106$	$46546832455691959/748268928$	$1.13125$	$5.92771$	$[0, 0, 0, -1480603404, -21928059286000]$	\(y^2=x^3-1480603404x-21928059286000\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$
310464.oi1	310464oi2	310464.oi	310464oi	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{25} \cdot 3^{18} \cdot 7^{9} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$4$	$2$	$1$	$115605504$	$3.884106$	$46546832455691959/748268928$	$1.13125$	$5.92771$	$[0, 0, 0, -1480603404, 21928059286000]$	\(y^2=x^3-1480603404x+21928059286000\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$	$1$

  Download displayed columns for results to