Elliptic curve search results

Results (14 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
2159.a1	2159a2	2159.a	2159a	$2$	$2$	\( 17 \cdot 127 \)	\( 17 \cdot 127^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$1$		$0$	$272$	$-0.095708$	$75418890625/274193$	$0.95730$	$3.26234$	$1$	$[1, 1, 1, -88, 280]$	\(y^2+xy+y=x^3+x^2-88x+280\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$
19431.d1	19431e2	19431.d	19431e	$2$	$2$	\( 3^{2} \cdot 17 \cdot 127 \)	\( 3^{6} \cdot 17 \cdot 127^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$1$		$0$	$6528$	$0.453598$	$75418890625/274193$	$0.95730$	$3.20397$	$1$	$[1, -1, 0, -792, -8357]$	\(y^2+xy=x^3-x^2-792x-8357\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$
34544.b1	34544d2	34544.b	34544d	$2$	$2$	\( 2^{4} \cdot 17 \cdot 127 \)	\( 2^{12} \cdot 17 \cdot 127^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$4.266119860$	$1$		$9$	$17408$	$0.597439$	$75418890625/274193$	$0.95730$	$3.19274$	$1$	$[0, 1, 0, -1408, -20748]$	\(y^2=x^3+x^2-1408x-20748\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[(-22, 8), (-574/5, 224/5)]$	$1$
36703.a1	36703a2	36703.a	36703a	$2$	$2$	\( 17^{2} \cdot 127 \)	\( 17^{7} \cdot 127^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$1$		$0$	$78336$	$1.320898$	$75418890625/274193$	$0.95730$	$4.00030$	$1$	$[1, 0, 0, -25438, 1554579]$	\(y^2+xy=x^3-25438x+1554579\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$
53975.d1	53975c2	53975.d	53975c	$2$	$2$	\( 5^{2} \cdot 17 \cdot 127 \)	\( 5^{6} \cdot 17 \cdot 127^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$1$		$0$	$39168$	$0.709011$	$75418890625/274193$	$0.95730$	$3.18485$	$1$	$[1, 0, 1, -2201, 39423]$	\(y^2+xy+y=x^3-2201x+39423\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$
105791.a1	105791c2	105791.a	105791c	$2$	$2$	\( 7^{2} \cdot 17 \cdot 127 \)	\( 7^{6} \cdot 17 \cdot 127^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$1$		$0$	$97920$	$0.877247$	$75418890625/274193$	$0.95730$	$3.17409$	$1$	$[1, 0, 0, -4313, -109040]$	\(y^2+xy=x^3-4313x-109040\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$
138176.b1	138176k2	138176.b	138176k	$2$	$2$	\( 2^{6} \cdot 17 \cdot 127 \)	\( 2^{18} \cdot 17 \cdot 127^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$3.298938689$	$1$		$11$	$139264$	$0.944013$	$75418890625/274193$	$0.95730$	$3.17017$	$1$	$[0, 1, 0, -5633, 160351]$	\(y^2=x^3+x^2-5633x+160351\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[(59, 192), (91, 640)]$	$1$
138176.o1	138176h2	138176.o	138176h	$2$	$2$	\( 2^{6} \cdot 17 \cdot 127 \)	\( 2^{18} \cdot 17 \cdot 127^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$4$	$2$	$1$	$139264$	$0.944013$	$75418890625/274193$	$0.95730$	$3.17017$	$1$	$[0, -1, 0, -5633, -160351]$	\(y^2=x^3-x^2-5633x-160351\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$
261239.a1	261239a2	261239.a	261239a	$2$	$2$	\( 11^{2} \cdot 17 \cdot 127 \)	\( 11^{6} \cdot 17 \cdot 127^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$28.95183582$	$1$		$0$	$348160$	$1.103239$	$75418890625/274193$	$0.95730$	$3.16148$	$1$	$[1, 1, 0, -10650, -426169]$	\(y^2+xy=x^3+x^2-10650x-426169\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[(36801749473051/271170, 213365268313068533741/271170)]$	$1$
274193.a1	274193a2	274193.a	274193a	$2$	$2$	\( 17 \cdot 127^{2} \)	\( 17 \cdot 127^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$1$		$0$	$4386816$	$2.326385$	$75418890625/274193$	$0.95730$	$4.32145$	$1$	$[1, 0, 0, -1419688, -649154625]$	\(y^2+xy=x^3-1419688x-649154625\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$
310896.p1	310896p2	310896.p	310896p	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 17 \cdot 127 \)	\( 2^{12} \cdot 3^{6} \cdot 17 \cdot 127^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$1$		$1$	$417792$	$1.146746$	$75418890625/274193$	$0.95730$	$3.15925$	$1$	$[0, 0, 0, -12675, 547522]$	\(y^2=x^3-12675x+547522\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$
330327.h1	330327h2	330327.h	330327h	$2$	$2$	\( 3^{2} \cdot 17^{2} \cdot 127 \)	\( 3^{6} \cdot 17^{7} \cdot 127^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$14.50721648$	$1$		$0$	$1880064$	$1.870205$	$75418890625/274193$	$0.95730$	$3.82734$	$1$	$[1, -1, 0, -228942, -41973633]$	\(y^2+xy=x^3-x^2-228942x-41973633\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[(139510071/494, 412301314485/494)]$	$1$
364871.i1	364871i2	364871.i	364871i	$2$	$2$	\( 13^{2} \cdot 17 \cdot 127 \)	\( 13^{6} \cdot 17 \cdot 127^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$1$		$0$	$626688$	$1.186766$	$75418890625/274193$	$0.95730$	$3.15726$	$1$	$[1, 1, 0, -14875, 689928]$	\(y^2+xy=x^3+x^2-14875x+689928\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$
485775.k1	485775k2	485775.k	485775k	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 17 \cdot 127 \)	\( 3^{6} \cdot 5^{6} \cdot 17 \cdot 127^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8636$	$12$	$0$	$1$	$1$		$0$	$940032$	$1.258318$	$75418890625/274193$	$0.95730$	$3.15383$	$1$	$[1, -1, 1, -19805, -1064428]$	\(y^2+xy+y=x^3-x^2-19805x-1064428\)	2.3.0.a.1, 34.6.0.a.1, 508.6.0.?, 8636.12.0.?	$[ ]$	$1$

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