Elliptic curve search results

Results (18 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
3698.a2	3698a1	3698.a	3698a	$2$	$3$	\( 2 \cdot 43^{2} \)	\( 2^{4} \cdot 43^{8} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.4.0.2, 3.8.0.1	2Cn, 3B.1.1	$516$	$96$	$2$	$9.284399057$	$1$		$2$	$14448$	$1.494524$	$294937/16$	$0.85413$	$5.19553$	$1$	$[1, 0, 1, -31472, 2043118]$	\(y^2+xy+y=x^3-31472x+2043118\)	2.2.0.a.1, 3.8.0-3.a.1.2, 4.4.0-2.a.1.1, 6.16.0-6.a.1.2, 12.32.0-12.a.2.4, $\ldots$	$[(-791/11, 1999557/11)]$	$1$
3698.b2	3698b1	3698.b	3698b	$2$	$3$	\( 2 \cdot 43^{2} \)	\( 2^{4} \cdot 43^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$516$	$96$	$2$	$0.396662854$	$1$		$4$	$336$	$-0.386076$	$294937/16$	$0.85413$	$2.44864$	$1$	$[1, 1, 1, -17, -33]$	\(y^2+xy+y=x^3+x^2-17x-33\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 86.6.0.?, $\ldots$	$[(-3, 2)]$	$1$
29584.g2	29584j1	29584.g	29584j	$2$	$3$	\( 2^{4} \cdot 43^{2} \)	\( 2^{16} \cdot 43^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.4.0.2, 3.4.0.1	2Cn, 3B	$516$	$96$	$2$	$1$	$4$	$2$	$0$	$346752$	$2.187672$	$294937/16$	$0.85413$	$4.95405$	$1$	$[0, -1, 0, -503544, -130759568]$	\(y^2=x^3-x^2-503544x-130759568\)	2.2.0.a.1, 3.4.0.a.1, 4.4.0-2.a.1.1, 6.8.0.a.1, 12.32.0-12.a.2.2, $\ldots$	$[ ]$	$1$
29584.j2	29584l1	29584.j	29584l	$2$	$3$	\( 2^{4} \cdot 43^{2} \)	\( 2^{16} \cdot 43^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$516$	$96$	$2$	$0.584062701$	$1$		$4$	$8064$	$0.307071$	$294937/16$	$0.85413$	$2.76199$	$1$	$[0, 1, 0, -272, 1556]$	\(y^2=x^3+x^2-272x+1556\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 86.6.0.?, $\ldots$	$[(2, 32)]$	$1$
33282.n2	33282o1	33282.n	33282o	$2$	$3$	\( 2 \cdot 3^{2} \cdot 43^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 43^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$516$	$96$	$2$	$1.287210826$	$1$		$4$	$10080$	$0.163230$	$294937/16$	$0.85413$	$2.56498$	$1$	$[1, -1, 0, -153, 733]$	\(y^2+xy=x^3-x^2-153x+733\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 86.6.0.?, $\ldots$	$[(6, -1)]$	$1$
33282.s2	33282y1	33282.s	33282y	$2$	$3$	\( 2 \cdot 3^{2} \cdot 43^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 43^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.8.0.2	2Cn, 3B.1.2	$516$	$96$	$2$	$2.396678579$	$1$		$0$	$433440$	$2.043831$	$294937/16$	$0.85413$	$4.73225$	$1$	$[1, -1, 1, -283244, -55164193]$	\(y^2+xy+y=x^3-x^2-283244x-55164193\)	2.2.0.a.1, 3.8.0-3.a.1.1, 6.16.0-6.a.1.1, 12.32.0-12.a.2.1, 86.6.0.?, $\ldots$	$[(-2309/3, 23789/3)]$	$1$
92450.n2	92450f1	92450.n	92450f	$2$	$3$	\( 2 \cdot 5^{2} \cdot 43^{2} \)	\( 2^{4} \cdot 5^{6} \cdot 43^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$2580$	$96$	$2$	$1$	$1$		$0$	$36288$	$0.418643$	$294937/16$	$0.85413$	$2.60385$	$1$	$[1, 0, 1, -426, -3252]$	\(y^2+xy+y=x^3-426x-3252\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 86.6.0.?, $\ldots$	$[ ]$	$1$
92450.ba2	92450u1	92450.ba	92450u	$2$	$3$	\( 2 \cdot 5^{2} \cdot 43^{2} \)	\( 2^{4} \cdot 5^{6} \cdot 43^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$2580$	$96$	$2$	$1$	$1$		$0$	$1560384$	$2.299244$	$294937/16$	$0.85413$	$4.57747$	$1$	$[1, 1, 1, -786788, 255389781]$	\(y^2+xy+y=x^3+x^2-786788x+255389781\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 15.8.0-3.a.1.2, $\ldots$	$[ ]$	$1$
118336.h2	118336f1	118336.h	118336f	$2$	$3$	\( 2^{6} \cdot 43^{2} \)	\( 2^{22} \cdot 43^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.4.0.1, 3.4.0.1	2Cn, 3B	$1032$	$96$	$2$	$4.743173610$	$1$		$2$	$2774016$	$2.534245$	$294937/16$	$0.85413$	$4.72215$	$1$	$[0, -1, 0, -2014177, 1048090721]$	\(y^2=x^3-x^2-2014177x+1048090721\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 8.4.0-2.a.1.1, 12.16.0.a.2, $\ldots$	$[(1801, 57088)]$	$1$
118336.p2	118336bi1	118336.p	118336bi	$2$	$3$	\( 2^{6} \cdot 43^{2} \)	\( 2^{22} \cdot 43^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$1032$	$96$	$2$	$1.486817013$	$1$		$2$	$64512$	$0.653645$	$294937/16$	$0.85413$	$2.79024$	$1$	$[0, -1, 0, -1089, 13537]$	\(y^2=x^3-x^2-1089x+13537\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 86.6.0.?, $\ldots$	$[(69, 512)]$	$1$
118336.x2	118336x1	118336.x	118336x	$2$	$3$	\( 2^{6} \cdot 43^{2} \)	\( 2^{22} \cdot 43^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.4.0.1, 3.4.0.1	2Cn, 3B	$1032$	$96$	$2$	$1$	$1$		$0$	$2774016$	$2.534245$	$294937/16$	$0.85413$	$4.72215$	$1$	$[0, 1, 0, -2014177, -1048090721]$	\(y^2=x^3+x^2-2014177x-1048090721\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 8.4.0-2.a.1.1, 12.16.0.a.2, $\ldots$	$[ ]$	$1$
118336.bf2	118336m1	118336.bf	118336m	$2$	$3$	\( 2^{6} \cdot 43^{2} \)	\( 2^{22} \cdot 43^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$1032$	$96$	$2$	$1$	$1$		$0$	$64512$	$0.653645$	$294937/16$	$0.85413$	$2.79024$	$1$	$[0, 1, 0, -1089, -13537]$	\(y^2=x^3+x^2-1089x-13537\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 86.6.0.?, $\ldots$	$[ ]$	$1$
181202.a2	181202f1	181202.a	181202f	$2$	$3$	\( 2 \cdot 7^{2} \cdot 43^{2} \)	\( 2^{4} \cdot 7^{6} \cdot 43^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$3612$	$96$	$2$	$1$	$1$		$0$	$5461344$	$2.467480$	$294937/16$	$0.85413$	$4.48979$	$1$	$[1, 1, 0, -1542104, -702331664]$	\(y^2+xy=x^3+x^2-1542104x-702331664\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 21.8.0-3.a.1.1, $\ldots$	$[ ]$	$1$
181202.g2	181202d1	181202.g	181202d	$2$	$3$	\( 2 \cdot 7^{2} \cdot 43^{2} \)	\( 2^{4} \cdot 7^{6} \cdot 43^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$3612$	$96$	$2$	$1$	$1$		$0$	$127008$	$0.586879$	$294937/16$	$0.85413$	$2.62587$	$1$	$[1, 0, 0, -834, 8756]$	\(y^2+xy=x^3-834x+8756\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 86.6.0.?, $\ldots$	$[ ]$	$1$
266256.g2	266256g1	266256.g	266256g	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 43^{2} \)	\( 2^{16} \cdot 3^{6} \cdot 43^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$516$	$96$	$2$	$10.01646767$	$1$		$0$	$10402560$	$2.736977$	$294937/16$	$0.85413$	$4.61036$	$1$	$[0, 0, 0, -4531899, 3535040234]$	\(y^2=x^3-4531899x+3535040234\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.32.0-12.a.2.3, 86.6.0.?, $\ldots$	$[(-119395/7, 3611936/7)]$	$1$
266256.cv2	266256cv1	266256.cv	266256cv	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 43^{2} \)	\( 2^{16} \cdot 3^{6} \cdot 43^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$516$	$96$	$2$	$6.349236525$	$1$		$6$	$241920$	$0.856377$	$294937/16$	$0.85413$	$2.80386$	$1$	$[0, 0, 0, -2451, -44462]$	\(y^2=x^3-2451x-44462\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 86.6.0.?, $\ldots$	$[(57, 32), (-33, 22)]$	$1$
447458.h2	447458h1	447458.h	447458h	$2$	$3$	\( 2 \cdot 11^{2} \cdot 43^{2} \)	\( 2^{4} \cdot 11^{6} \cdot 43^{2} \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$5676$	$96$	$2$	$1.374759755$	$1$		$28$	$483840$	$0.812871$	$294937/16$	$0.85413$	$2.65186$	$1$	$[1, 1, 0, -2059, 33389]$	\(y^2+xy=x^3+x^2-2059x+33389\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 86.6.0.?, $\ldots$	$[(50, 217), (17, 52), (83, 624)]$	$1$
447458.bj2	447458bj1	447458.bj	447458bj	$2$	$3$	\( 2 \cdot 11^{2} \cdot 43^{2} \)	\( 2^{4} \cdot 11^{6} \cdot 43^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$5676$	$96$	$2$	$13.19285216$	$1$		$0$	$20805120$	$2.693470$	$294937/16$	$0.85413$	$4.38629$	$1$	$[1, 0, 0, -3808054, -2723198444]$	\(y^2+xy=x^3-3808054x-2723198444\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 33.8.0-3.a.1.2, $\ldots$	$[(10730100/31, 34406585594/31)]$	$1$

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