Elliptic curves over $\Q$ of conductor 40733

Results (16 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
40733.a1	40733e1	40733.a	40733e	$1$	$1$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7^{10} \cdot 11^{2} \cdot 23^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.2.0.1		$616$	$4$	$0$	$1.786006386$	$1$		$4$	$2627520$	$2.991467$	$-14429645772301489/34179505129$	$0.94845$	$5.86880$	$[1, 0, 0, -21699591, 38984528554]$	\(y^2+xy=x^3-21699591x+38984528554\)	4.2.0.a.1, 616.4.0.?	$[(1587, 91645)]$
40733.b1	40733i1	40733.b	40733i	$1$	$1$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7^{10} \cdot 11^{2} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.2.0.1		$14168$	$4$	$0$	$0.644412649$	$1$		$4$	$114240$	$1.423719$	$-14429645772301489/34179505129$	$0.94845$	$4.09647$	$[1, 0, 0, -41020, -3207687]$	\(y^2+xy=x^3-41020x-3207687\)	4.2.0.a.1, 14168.4.0.?	$[(259, 1757)]$
40733.c1	40733j2	40733.c	40733j	$2$	$2$	\( 7 \cdot 11 \cdot 23^{2} \)	\( 7^{2} \cdot 11^{4} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$644$	$12$	$0$	$1.683612979$	$1$		$2$	$422400$	$1.681356$	$128100283921/16500407$	$1.04025$	$4.18181$	$[1, 0, 0, -55556, 4439353]$	\(y^2+xy=x^3-55556x+4439353\)	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(-48, 2669)]$
40733.c2	40733j1	40733.c	40733j	$2$	$2$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7 \cdot 11^{2} \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$644$	$12$	$0$	$3.367225959$	$1$		$1$	$211200$	$1.334784$	$109902239/448063$	$0.85315$	$3.68611$	$[1, 0, 0, 5279, 363408]$	\(y^2+xy=x^3+5279x+363408\)	2.3.0.a.1, 14.6.0.b.1, 92.6.0.?, 644.12.0.?	$[(383/2, 10197/2)]$
40733.d1	40733d1	40733.d	40733d	$1$	$1$	\( 7 \cdot 11 \cdot 23^{2} \)	\( 7 \cdot 11 \cdot 23^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$7084$	$2$	$0$	$0.596737210$	$1$		$4$	$33792$	$0.937117$	$24137569/1771$	$0.82777$	$3.37381$	$[1, 1, 1, -3185, 63324]$	\(y^2+xy+y=x^3+x^2-3185x+63324\)	7084.2.0.?	$[(-56, 292)]$
40733.e1	40733k1	40733.e	40733k	$1$	$1$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7^{2} \cdot 11 \cdot 23^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$48488$	$0.781094$	$884736/539$	$1.02512$	$3.06233$	$[0, 0, 1, 1058, -3042]$	\(y^2+y=x^3+1058x-3042\)	22.2.0.a.1	$[]$
40733.f1	40733b1	40733.f	40733b	$2$	$3$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7^{3} \cdot 11 \cdot 23^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$10626$	$16$	$0$	$1.800116175$	$1$		$2$	$76032$	$1.253372$	$-799178752/86779$	$0.79027$	$3.71972$	$[0, 1, 1, -10227, -437253]$	\(y^2+y=x^3+x^2-10227x-437253\)	3.4.0.a.1, 69.8.0-3.a.1.2, 462.8.0.?, 3542.2.0.?, 10626.16.0.?	$[(245, 3438)]$
40733.f2	40733b2	40733.f	40733b	$2$	$3$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7 \cdot 11^{3} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$10626$	$16$	$0$	$0.600038725$	$1$		$6$	$228096$	$1.802679$	$194305753088/113359939$	$0.95045$	$4.22106$	$[0, 1, 1, 63833, 581072]$	\(y^2+y=x^3+x^2+63833x+581072\)	3.4.0.a.1, 69.8.0-3.a.1.1, 462.8.0.?, 3542.2.0.?, 10626.16.0.?	$[(268, 6083)]$
40733.g1	40733a1	40733.g	40733a	$3$	$9$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7^{2} \cdot 11 \cdot 23^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$31878$	$144$	$3$	$9.419022159$	$1$		$0$	$83160$	$1.272747$	$-78843215872/539$	$1.00604$	$4.13609$	$[0, 1, 1, -47257, -3969915]$	\(y^2+y=x^3+x^2-47257x-3969915\)	3.4.0.a.1, 9.12.0.a.1, 22.2.0.a.1, 63.36.0.e.1, 66.8.0.a.1, $\ldots$	$[(29451/5, 4963249/5)]$
40733.g2	40733a2	40733.g	40733a	$3$	$9$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7^{6} \cdot 11^{3} \cdot 23^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$31878$	$144$	$3$	$3.139674053$	$1$		$2$	$249480$	$1.822054$	$-13278380032/156590819$	$1.06522$	$4.25677$	$[0, 1, 1, -26097, -7511570]$	\(y^2+y=x^3+x^2-26097x-7511570\)	3.12.0.a.1, 22.2.0.a.1, 63.36.0.b.1, 66.24.1.b.1, 69.24.0-3.a.1.1, $\ldots$	$[(286, 2915)]$
40733.g3	40733a3	40733.g	40733a	$3$	$9$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7^{2} \cdot 11^{9} \cdot 23^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$31878$	$144$	$3$	$1.046558017$	$1$		$4$	$748440$	$2.371361$	$9463555063808/115539436859$	$1.06593$	$4.86981$	$[0, 1, 1, 233113, 194283415]$	\(y^2+y=x^3+x^2+233113x+194283415\)	3.4.0.a.1, 9.12.0.a.1, 22.2.0.a.1, 63.36.0.e.2, 66.8.0.a.1, $\ldots$	$[(-421, 4658)]$
40733.h1	40733h1	40733.h	40733h	$1$	$1$	\( 7 \cdot 11 \cdot 23^{2} \)	\( 7 \cdot 11 \cdot 23^{11} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$7084$	$2$	$0$	$3.271710612$	$1$		$2$	$675840$	$1.943653$	$1794942305577/495598411$	$0.88792$	$4.43051$	$[1, -1, 0, -133936, 13676113]$	\(y^2+xy=x^3-x^2-133936x+13676113\)	7084.2.0.?	$[(-408, 733)]$
40733.i1	40733f2	40733.i	40733f	$2$	$2$	\( 7 \cdot 11 \cdot 23^{2} \)	\( 7^{6} \cdot 11 \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$308$	$12$	$0$	$10.61977163$	$1$		$0$	$147840$	$1.481728$	$15124197817/1294139$	$0.97750$	$3.98053$	$[1, 1, 0, -27254, -1610035]$	\(y^2+xy=x^3+x^2-27254x-1610035\)	2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.?	$[(-146915/44, 17576285/44)]$
40733.i2	40733f1	40733.i	40733f	$2$	$2$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7^{3} \cdot 11^{2} \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$308$	$12$	$0$	$5.309885816$	$1$		$1$	$73920$	$1.135155$	$4657463/41503$	$0.89262$	$3.47007$	$[1, 1, 0, 1841, -114552]$	\(y^2+xy=x^3+x^2+1841x-114552\)	2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.?	$[(16911/2, 2182671/2)]$
40733.j1	40733c1	40733.j	40733c	$1$	$1$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7 \cdot 11 \cdot 23^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$308$	$2$	$0$	$13.70641170$	$1$		$0$	$88320$	$1.148121$	$-77625/77$	$0.65353$	$3.51793$	$[1, -1, 0, -3802, -147715]$	\(y^2+xy=x^3-x^2-3802x-147715\)	308.2.0.?	$[(45936076/567, 258017536153/567)]$
40733.k1	40733g1	40733.k	40733g	$1$	$1$	\( 7 \cdot 11 \cdot 23^{2} \)	\( - 7 \cdot 11 \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$308$	$2$	$0$	$3.801650364$	$1$		$0$	$3840$	$-0.419627$	$-77625/77$	$0.65353$	$1.74559$	$[1, -1, 0, -7, 14]$	\(y^2+xy=x^3-x^2-7x+14\)	308.2.0.?	$[(-26/3, 92/3)]$