Elliptic curves over $\Q$ of conductor 78897

Results (25 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
78897.a1	78897a1	78897.a	78897a	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{2} \cdot 7 \cdot 13^{3} \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$2.342159669$	$1$		$2$	$635904$	$1.554766$	$-325660672/40000779$	$0.89294$	$3.72149$	$[0, -1, 1, -4142, -1497130]$	\(y^2+y=x^3-x^2-4142x-1497130\)	182.2.0.?	$[(227, 3034)]$
78897.b1	78897j1	78897.b	78897j	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{4} \cdot 7^{3} \cdot 13 \cdot 17^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$0.845111858$	$1$		$4$	$236544$	$1.208393$	$-2019487744/361179$	$0.90207$	$3.43163$	$[0, 1, 1, -7610, 289832]$	\(y^2+y=x^3+x^2-7610x+289832\)	182.2.0.?	$[(79, 433)]$
78897.c1	78897e1	78897.c	78897e	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{4} \cdot 7 \cdot 13 \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$1$	$1$		$0$	$13248$	$-0.023037$	$-155198593/7371$	$0.79085$	$2.18213$	$[1, 1, 1, -74, -286]$	\(y^2+xy+y=x^3+x^2-74x-286\)	182.2.0.?	$[]$
78897.d1	78897b1	78897.d	78897b	$2$	$2$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3^{5} \cdot 7 \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$18564$	$12$	$0$	$1$	$4$	$2$	$1$	$645120$	$1.665255$	$10418796526321/6390657$	$0.87866$	$4.16587$	$[1, 1, 1, -131501, 18289946]$	\(y^2+xy+y=x^3+x^2-131501x+18289946\)	2.3.0.a.1, 68.6.0.b.1, 546.6.0.?, 18564.12.0.?	$[]$
78897.d2	78897b2	78897.d	78897b	$2$	$2$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{10} \cdot 7^{2} \cdot 13^{2} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$18564$	$12$	$0$	$1$	$1$		$0$	$1290240$	$2.011826$	$-5602762882081/8312741073$	$0.89460$	$4.22356$	$[1, 1, 1, -106936, 25364666]$	\(y^2+xy+y=x^3+x^2-106936x+25364666\)	2.3.0.a.1, 68.6.0.a.1, 1092.6.0.?, 18564.12.0.?	$[]$
78897.e1	78897i1	78897.e	78897i	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{4} \cdot 7 \cdot 13 \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$1.385398855$	$1$		$2$	$225216$	$1.393570$	$-155198593/7371$	$0.79085$	$3.68971$	$[1, 0, 0, -21392, -1254501]$	\(y^2+xy=x^3-21392x-1254501\)	182.2.0.?	$[(313, 4612)]$
78897.f1	78897m4	78897.f	78897m	$4$	$4$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3 \cdot 7 \cdot 13 \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$37128$	$48$	$0$	$1$	$16$	$2$	$0$	$1474560$	$2.238548$	$1677087406638588673/4641$	$0.95144$	$5.22911$	$[1, 0, 0, -7153334, -7364546781]$	\(y^2+xy=x^3-7153334x-7364546781\)	2.3.0.a.1, 4.12.0-4.c.1.2, 136.24.0.?, 2184.24.0.?, 9282.6.0.?, $\ldots$	$[]$
78897.f2	78897m2	78897.f	78897m	$4$	$4$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3^{2} \cdot 7^{2} \cdot 13^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$18564$	$48$	$0$	$1$	$4$	$2$	$2$	$737280$	$1.891975$	$409460675852593/21538881$	$0.90509$	$4.49145$	$[1, 0, 0, -447089, -115095936]$	\(y^2+xy=x^3-447089x-115095936\)	2.6.0.a.1, 4.12.0-2.a.1.1, 68.24.0-68.a.1.1, 1092.24.0.?, 18564.48.0.?	$[]$
78897.f3	78897m3	78897.f	78897m	$4$	$4$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{4} \cdot 7^{4} \cdot 13^{4} \cdot 17^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$37128$	$48$	$0$	$1$	$1$		$2$	$1474560$	$2.238548$	$-345608484635233/94427721297$	$0.90966$	$4.51071$	$[1, 0, 0, -422524, -128297167]$	\(y^2+xy=x^3-422524x-128297167\)	2.3.0.a.1, 4.12.0-4.c.1.1, 68.24.0-68.h.1.2, 2184.24.0.?, 37128.48.0.?	$[]$
78897.f4	78897m1	78897.f	78897m	$4$	$4$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3 \cdot 7 \cdot 13 \cdot 17^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$37128$	$48$	$0$	$1$	$4$	$2$	$1$	$368640$	$1.545403$	$117433042273/22801233$	$0.84478$	$3.76807$	$[1, 0, 0, -29484, -1590897]$	\(y^2+xy=x^3-29484x-1590897\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 68.12.0-4.c.1.2, 136.24.0.?, $\ldots$	$[]$
78897.g1	78897l6	78897.g	78897l	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3^{2} \cdot 7^{2} \cdot 13^{8} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.56	2B	$74256$	$192$	$1$	$1$	$1$		$0$	$3538944$	$2.798492$	$7389727131216686257/6115533215337$	$0.95823$	$5.36063$	$[1, 0, 0, -11727337, -15447704248]$	\(y^2+xy=x^3-11727337x-15447704248\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 34.6.0.a.1, 68.24.0-68.g.1.1, $\ldots$	$[]$
78897.g2	78897l4	78897.g	78897l	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3^{4} \cdot 7^{4} \cdot 13^{4} \cdot 17^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.3	2Cs	$37128$	$192$	$1$	$1$	$1$		$2$	$1769472$	$2.451920$	$3275619238041697/1605271262049$	$0.94091$	$4.67586$	$[1, 0, 0, -894172, -127442305]$	\(y^2+xy=x^3-894172x-127442305\)	2.6.0.a.1, 4.24.0-4.b.1.2, 68.48.0-68.c.1.3, 104.48.0.?, 168.48.0.?, $\ldots$	$[]$
78897.g3	78897l2	78897.g	78897l	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3^{2} \cdot 7^{2} \cdot 13^{2} \cdot 17^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.24	2Cs	$37128$	$192$	$1$	$1$	$4$	$2$	$2$	$884736$	$2.105347$	$495909170514577/6224736609$	$0.90662$	$4.50844$	$[1, 0, 0, -476567, 125208720]$	\(y^2+xy=x^3-476567x+125208720\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.5, 68.24.0-4.b.1.3, 104.48.0.?, $\ldots$	$[]$
78897.g4	78897l1	78897.g	78897l	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3 \cdot 7 \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$74256$	$192$	$1$	$1$	$4$	$2$	$1$	$442368$	$1.758772$	$491411892194497/78897$	$0.90629$	$4.50763$	$[1, 0, 0, -475122, 126014163]$	\(y^2+xy=x^3-475122x+126014163\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 68.12.0-4.c.1.2, $\ldots$	$[]$
78897.g5	78897l3	78897.g	78897l	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3 \cdot 7 \cdot 13 \cdot 17^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$74256$	$192$	$1$	$1$	$16$	$2$	$0$	$1769472$	$2.451920$	$-2533811507137/1904381781393$	$0.97835$	$4.67634$	$[1, 0, 0, -82082, 326317173]$	\(y^2+xy=x^3-82082x+326317173\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 68.12.0-4.c.1.2, $\ldots$	$[]$
78897.g6	78897l5	78897.g	78897l	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{8} \cdot 7^{8} \cdot 13^{2} \cdot 17^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.46	2B	$74256$	$192$	$1$	$1$	$1$		$2$	$3538944$	$2.798492$	$158346567380527343/108665074944153$	$0.96311$	$5.01981$	$[1, 0, 0, 3257313, -975175542]$	\(y^2+xy=x^3+3257313x-975175542\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 68.24.0-68.h.1.2, 104.48.0.?, $\ldots$	$[]$
78897.h1	78897d1	78897.h	78897d	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{4} \cdot 7 \cdot 13 \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$5.258627702$	$1$		$2$	$230112$	$1.589481$	$-16595255296/7371$	$0.87048$	$4.09713$	$[0, -1, 1, -101535, -12423931]$	\(y^2+y=x^3-x^2-101535x-12423931\)	182.2.0.?	$[(393, 2866)]$
78897.i1	78897k1	78897.i	78897k	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{4} \cdot 7 \cdot 13 \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$1$	$1$		$0$	$13536$	$0.172874$	$-16595255296/7371$	$0.87048$	$2.58956$	$[0, 1, 1, -351, -2653]$	\(y^2+y=x^3+x^2-351x-2653\)	182.2.0.?	$[]$
78897.j1	78897g1	78897.j	78897g	$2$	$2$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3^{3} \cdot 7 \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$18564$	$12$	$0$	$6.873776699$	$1$		$1$	$221184$	$1.287888$	$10431681625/710073$	$0.81522$	$3.55337$	$[1, 1, 0, -13155, 540072]$	\(y^2+xy=x^3+x^2-13155x+540072\)	2.3.0.a.1, 68.6.0.b.1, 546.6.0.?, 18564.12.0.?	$[(952/3, 14456/3)]$
78897.j2	78897g2	78897.j	78897g	$2$	$2$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{6} \cdot 7^{2} \cdot 13^{2} \cdot 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$18564$	$12$	$0$	$3.436888349$	$1$		$2$	$442368$	$1.634460$	$6804992375/102626433$	$0.87463$	$3.80116$	$[1, 1, 0, 11410, 2352969]$	\(y^2+xy=x^3+x^2+11410x+2352969\)	2.3.0.a.1, 68.6.0.a.1, 1092.6.0.?, 18564.12.0.?	$[(320, 6077)]$
78897.k1	78897c1	78897.k	78897c	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{2} \cdot 7 \cdot 13 \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$1$	$1$		$0$	$13248$	$-0.287873$	$69632/819$	$0.70887$	$1.75408$	$[0, -1, 1, 6, -25]$	\(y^2+y=x^3-x^2+6x-25\)	182.2.0.?	$[]$
78897.l1	78897f1	78897.l	78897f	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{8} \cdot 7^{7} \cdot 13^{3} \cdot 17^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$1$	$1$		$0$	$3483648$	$2.607117$	$1811564780171264/11870974573731$	$1.04721$	$4.83036$	$[0, -1, 1, 733964, -777871065]$	\(y^2+y=x^3-x^2+733964x-777871065\)	182.2.0.?	$[]$
78897.m1	78897h1	78897.m	78897h	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{6} \cdot 7 \cdot 13 \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$45.01233101$	$1$		$0$	$1188864$	$1.993389$	$-2731787761881088/19171971$	$0.92571$	$4.65976$	$[0, -1, 1, -841664, -296926513]$	\(y^2+y=x^3-x^2-841664x-296926513\)	182.2.0.?	$[(2939969214527949825845/589935158, 158417551420918680944908195898297/589935158)]$
78897.n1	78897n1	78897.n	78897n	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{22} \cdot 7 \cdot 13 \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$1$	$1$		$0$	$9427968$	$2.980309$	$-1302227927110660096/825290486657091$	$0.97155$	$5.27226$	$[0, 1, 1, -6574846, 9390313969]$	\(y^2+y=x^3+x^2-6574846x+9390313969\)	182.2.0.?	$[]$
78897.o1	78897o1	78897.o	78897o	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{2} \cdot 7 \cdot 13 \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$182$	$2$	$0$	$26.86680427$	$1$		$0$	$225216$	$1.128733$	$69632/819$	$0.70887$	$3.26165$	$[0, 1, 1, 1638, -111589]$	\(y^2+y=x^3+x^2+1638x-111589\)	182.2.0.?	$[(588781373409/79312, 465235259061814831/79312)]$