Elliptic curve search results

Results (29 matches)

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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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
966.k1	966j1	966.k	966j	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{9} \cdot 3 \cdot 7^{11} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3864$	$2$	$0$	$1$	$1$		$0$	$3960$	$1.344131$	$83228502970940543/69854999176704$	$1.01004$	$5.66848$	$1$	$[1, 0, 0, 9096, 224832]$	\(y^2+xy=x^3+9096x+224832\)	3864.2.0.?	$[ ]$	$1$
2898.a1	2898f1	2898.a	2898f	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7 \cdot 23 \)	\( - 2^{9} \cdot 3^{7} \cdot 7^{11} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$31680$	$1.893436$	$83228502970940543/69854999176704$	$1.01004$	$5.71416$	$1$	$[1, -1, 0, 81864, -6070464]$	\(y^2+xy=x^3-x^2+81864x-6070464\)	3864.2.0.?	$[ ]$	$1$
6762.y1	6762bd1	6762.y	6762bd	$1$	$1$	\( 2 \cdot 3 \cdot 7^{2} \cdot 23 \)	\( - 2^{9} \cdot 3 \cdot 7^{17} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$190080$	$2.317085$	$83228502970940543/69854999176704$	$1.01004$	$5.74163$	$1$	$[1, 1, 1, 445703, -76671673]$	\(y^2+xy+y=x^3+x^2+445703x-76671673\)	3864.2.0.?	$[ ]$	$1$
7728.j1	7728m1	7728.j	7728m	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{21} \cdot 3 \cdot 7^{11} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$0.562420442$	$1$		$4$	$95040$	$2.037277$	$83228502970940543/69854999176704$	$1.01004$	$5.28094$	$1$	$[0, -1, 0, 145536, -14389248]$	\(y^2=x^3-x^2+145536x-14389248\)	3864.2.0.?	$[(4544, 307328)]$	$1$
20286.bb1	20286ba1	20286.bb	20286ba	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	\( - 2^{9} \cdot 3^{7} \cdot 7^{17} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$6.494109301$	$1$		$2$	$1520640$	$2.866390$	$83228502970940543/69854999176704$	$1.01004$	$5.77025$	$1$	$[1, -1, 0, 4011327, 2074146493]$	\(y^2+xy=x^3-x^2+4011327x+2074146493\)	3864.2.0.?	$[(641, 69740)]$	$1$
22218.bd1	22218bj1	22218.bd	22218bj	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 23^{2} \)	\( - 2^{9} \cdot 3 \cdot 7^{11} \cdot 23^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$0.271724354$	$1$		$4$	$2090880$	$2.911877$	$83228502970940543/69854999176704$	$1.01004$	$5.77234$	$1$	$[1, 0, 0, 4811773, -2725907391]$	\(y^2+xy=x^3+4811773x-2725907391\)	3864.2.0.?	$[(1332, 77097)]$	$1$
23184.h1	23184ca1	23184.h	23184ca	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( - 2^{21} \cdot 3^{7} \cdot 7^{11} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$0.446362729$	$1$		$6$	$760320$	$2.586582$	$83228502970940543/69854999176704$	$1.01004$	$5.35953$	$1$	$[0, 0, 0, 1309821, 387199874]$	\(y^2=x^3+1309821x+387199874\)	3864.2.0.?	$[(775, 43218)]$	$1$
24150.u1	24150k1	24150.u	24150k	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{9} \cdot 3 \cdot 5^{6} \cdot 7^{11} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$427680$	$2.148849$	$83228502970940543/69854999176704$	$1.01004$	$4.81736$	$1$	$[1, 1, 0, 227400, 28104000]$	\(y^2+xy=x^3+x^2+227400x+28104000\)	3864.2.0.?	$[ ]$	$1$
30912.c1	30912g1	30912.c	30912g	$1$	$1$	\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{27} \cdot 3 \cdot 7^{11} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$760320$	$2.383850$	$83228502970940543/69854999176704$	$1.01004$	$4.97510$	$1$	$[0, -1, 0, 582143, 114531841]$	\(y^2=x^3-x^2+582143x+114531841\)	3864.2.0.?	$[ ]$	$1$
30912.bj1	30912ci1	30912.bj	30912ci	$1$	$1$	\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{27} \cdot 3 \cdot 7^{11} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$760320$	$2.383850$	$83228502970940543/69854999176704$	$1.01004$	$4.97510$	$1$	$[0, 1, 0, 582143, -114531841]$	\(y^2=x^3+x^2+582143x-114531841\)	3864.2.0.?	$[ ]$	$1$
54096.bv1	54096cy1	54096.bv	54096cy	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( - 2^{21} \cdot 3 \cdot 7^{17} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$4561920$	$3.010231$	$83228502970940543/69854999176704$	$1.01004$	$5.40932$	$1$	$[0, 1, 0, 7131248, 4921249556]$	\(y^2=x^3+x^2+7131248x+4921249556\)	3864.2.0.?	$[ ]$	$1$
66654.ba1	66654ba1	66654.ba	66654ba	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7 \cdot 23^{2} \)	\( - 2^{9} \cdot 3^{7} \cdot 7^{11} \cdot 23^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$16727040$	$3.461185$	$83228502970940543/69854999176704$	$1.01004$	$5.79485$	$1$	$[1, -1, 0, 43305957, 73599499557]$	\(y^2+xy=x^3-x^2+43305957x+73599499557\)	3864.2.0.?	$[ ]$	$1$
72450.ee1	72450er1	72450.ee	72450er	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{9} \cdot 3^{7} \cdot 5^{6} \cdot 7^{11} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$0.283548262$	$1$		$8$	$3421440$	$2.698154$	$83228502970940543/69854999176704$	$1.01004$	$4.93346$	$1$	$[1, -1, 1, 2046595, -756761403]$	\(y^2+xy+y=x^3-x^2+2046595x-756761403\)	3864.2.0.?	$[(575, 24408)]$	$1$
92736.ff1	92736bi1	92736.ff	92736bi	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( - 2^{27} \cdot 3^{7} \cdot 7^{11} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$4$	$2$	$0$	$6082560$	$2.933159$	$83228502970940543/69854999176704$	$1.01004$	$5.07354$	$1$	$[0, 0, 0, 5239284, -3097598992]$	\(y^2=x^3+5239284x-3097598992\)	3864.2.0.?	$[ ]$	$1$
92736.fi1	92736fr1	92736.fi	92736fr	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( - 2^{27} \cdot 3^{7} \cdot 7^{11} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1.329423927$	$1$		$4$	$6082560$	$2.933159$	$83228502970940543/69854999176704$	$1.01004$	$5.07354$	$1$	$[0, 0, 0, 5239284, 3097598992]$	\(y^2=x^3+5239284x+3097598992\)	3864.2.0.?	$[(-382, 32256)]$	$1$
116886.x1	116886x1	116886.x	116886x	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 11^{2} \cdot 23 \)	\( - 2^{9} \cdot 3 \cdot 7^{11} \cdot 11^{6} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$4.079065138$	$1$		$2$	$5068800$	$2.543079$	$83228502970940543/69854999176704$	$1.01004$	$4.57177$	$1$	$[1, 0, 1, 1100613, -298150778]$	\(y^2+xy+y=x^3+1100613x-298150778\)	3864.2.0.?	$[(15190, 1868933)]$	$1$
155526.ce1	155526bp1	155526.ce	155526bp	$1$	$1$	\( 2 \cdot 3 \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{9} \cdot 3 \cdot 7^{17} \cdot 23^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$100362240$	$3.884834$	$83228502970940543/69854999176704$	$1.01004$	$5.80939$	$1$	$[1, 1, 1, 235776876, 935222011989]$	\(y^2+xy+y=x^3+x^2+235776876x+935222011989\)	3864.2.0.?	$[ ]$	$1$
162288.gj1	162288cq1	162288.gj	162288cq	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	\( - 2^{21} \cdot 3^{7} \cdot 7^{17} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$18.07998765$	$1$		$0$	$36495360$	$3.559540$	$83228502970940543/69854999176704$	$1.01004$	$5.46341$	$1$	$[0, 0, 0, 64181229, -132809556782]$	\(y^2=x^3+64181229x-132809556782\)	3864.2.0.?	$[(61755342663/4777, 26856899198113334/4777)]$	$1$
163254.bh1	163254ca1	163254.bh	163254ca	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \cdot 23 \)	\( - 2^{9} \cdot 3 \cdot 7^{11} \cdot 13^{6} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$8886240$	$2.626606$	$83228502970940543/69854999176704$	$1.01004$	$4.52802$	$1$	$[1, 0, 1, 1537220, 492418682]$	\(y^2+xy+y=x^3+1537220x+492418682\)	3864.2.0.?	$[ ]$	$1$
169050.eb1	169050gr1	169050.eb	169050gr	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( - 2^{9} \cdot 3 \cdot 5^{6} \cdot 7^{17} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$29.46648176$	$1$		$0$	$20528640$	$3.121803$	$83228502970940543/69854999176704$	$1.01004$	$5.00853$	$1$	$[1, 0, 1, 11142574, -9606244252]$	\(y^2+xy+y=x^3+11142574x-9606244252\)	3864.2.0.?	$[(3435956159677624/1498317, 350745169101904478643071/1498317)]$	$1$
177744.f1	177744bn1	177744.f	177744bn	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23^{2} \)	\( - 2^{21} \cdot 3 \cdot 7^{11} \cdot 23^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$15.38146159$	$1$		$0$	$50181120$	$3.605026$	$83228502970940543/69854999176704$	$1.01004$	$5.46745$	$1$	$[0, -1, 0, 76988368, 174458073024]$	\(y^2=x^3-x^2+76988368x+174458073024\)	3864.2.0.?	$[(1049833672/383, 58708927772288/383)]$	$1$
193200.dz1	193200cc1	193200.dz	193200cc	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{21} \cdot 3 \cdot 5^{6} \cdot 7^{11} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$25$	$5$	$0$	$10264320$	$2.841995$	$83228502970940543/69854999176704$	$1.01004$	$4.67772$	$1$	$[0, 1, 0, 3638392, -1791379212]$	\(y^2=x^3+x^2+3638392x-1791379212\)	3864.2.0.?	$[ ]$	$1$
216384.ed1	216384eh1	216384.ed	216384eh	$1$	$1$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( - 2^{27} \cdot 3 \cdot 7^{17} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$21.06238493$	$1$		$0$	$36495360$	$3.356808$	$83228502970940543/69854999176704$	$1.01004$	$5.13744$	$1$	$[0, -1, 0, 28524991, 39341471457]$	\(y^2=x^3-x^2+28524991x+39341471457\)	3864.2.0.?	$[(1971745374336/5933, 2781543001899798171/5933)]$	$1$
216384.ii1	216384gm1	216384.ii	216384gm	$1$	$1$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( - 2^{27} \cdot 3 \cdot 7^{17} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$25$	$5$	$0$	$36495360$	$3.356808$	$83228502970940543/69854999176704$	$1.01004$	$5.13744$	$1$	$[0, 1, 0, 28524991, -39341471457]$	\(y^2=x^3+x^2+28524991x-39341471457\)	3864.2.0.?	$[ ]$	$1$
279174.bq1	279174bq1	279174.bq	279174bq	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 17^{2} \cdot 23 \)	\( - 2^{9} \cdot 3 \cdot 7^{11} \cdot 17^{6} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$0.294940706$	$1$		$4$	$19514880$	$2.760738$	$83228502970940543/69854999176704$	$1.01004$	$4.46264$	$1$	$[1, 1, 1, 2628738, 1101970875]$	\(y^2+xy+y=x^3+x^2+2628738x+1101970875\)	3864.2.0.?	$[(681, 56303)]$	$1$
348726.i1	348726i1	348726.i	348726i	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 19^{2} \cdot 23 \)	\( - 2^{9} \cdot 3 \cdot 7^{11} \cdot 19^{6} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$44.69359300$	$1$		$0$	$28512000$	$2.816349$	$83228502970940543/69854999176704$	$1.01004$	$4.43714$	$1$	$[1, 1, 0, 3283649, -1535555387]$	\(y^2+xy=x^3+x^2+3283649x-1535555387\)	3864.2.0.?	$[(129636454562636409153/490367953, 2302117508075059432715564503399/490367953)]$	$1$
350658.cn1	350658cn1	350658.cn	350658cn	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7 \cdot 11^{2} \cdot 23 \)	\( - 2^{9} \cdot 3^{7} \cdot 7^{11} \cdot 11^{6} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$0.365515927$	$1$		$6$	$40550400$	$3.092384$	$83228502970940543/69854999176704$	$1.01004$	$4.69466$	$1$	$[1, -1, 1, 9905521, 8050070999]$	\(y^2+xy+y=x^3-x^2+9905521x+8050070999\)	3864.2.0.?	$[(7791, 743158)]$	$1$
466578.p1	466578p1	466578.p	466578p	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 23^{2} \)	\( - 2^{9} \cdot 3^{7} \cdot 7^{17} \cdot 23^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$4$	$2$	$0$	$802897920$	$4.434135$	$83228502970940543/69854999176704$	$1.01004$	$5.82544$	$1$	$[1, -1, 0, 2121991884, -25248872331824]$	\(y^2+xy=x^3-x^2+2121991884x-25248872331824\)	3864.2.0.?	$[ ]$	$1$
489762.fj1	489762fj1	489762.fj	489762fj	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \cdot 23 \)	\( - 2^{9} \cdot 3^{7} \cdot 7^{11} \cdot 13^{6} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3864$	$2$	$0$	$1$	$1$		$0$	$71089920$	$3.175911$	$83228502970940543/69854999176704$	$1.01004$	$4.65145$	$1$	$[1, -1, 1, 13834984, -13295304421]$	\(y^2+xy+y=x^3-x^2+13834984x-13295304421\)	3864.2.0.?	$[ ]$	$1$

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