Elliptic curve search results

Results (18 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
1006.d1	1006d1	1006.d	1006d	$1$	$1$	\( 2 \cdot 503 \)	\( - 2^{10} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1006$	$2$	$0$	$0.106360665$	$1$		$8$	$120$	$-0.194395$	$-1349232625/515072$	$0.83497$	$3.11401$	$[1, 1, 1, -23, 45]$	\(y^2+xy+y=x^3+x^2-23x+45\)	1006.2.0.?	$[(3, 2)]$
8048.g1	8048e1	8048.g	8048e	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{22} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$2880$	$0.498752$	$-1349232625/515072$	$0.83497$	$3.31887$	$[0, 1, 0, -368, -3628]$	\(y^2=x^3+x^2-368x-3628\)	1006.2.0.?	$[]$
9054.d1	9054f1	9054.d	9054f	$1$	$1$	\( 2 \cdot 3^{2} \cdot 503 \)	\( - 2^{10} \cdot 3^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$3600$	$0.354911$	$-1349232625/515072$	$0.83497$	$3.08651$	$[1, -1, 0, -207, -1427]$	\(y^2+xy=x^3-x^2-207x-1427\)	1006.2.0.?	$[]$
25150.h1	25150b1	25150.h	25150b	$1$	$1$	\( 2 \cdot 5^{2} \cdot 503 \)	\( - 2^{10} \cdot 5^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.799508479$	$1$		$4$	$17280$	$0.610324$	$-1349232625/515072$	$0.83497$	$3.07779$	$[1, 0, 1, -576, 6798]$	\(y^2+xy+y=x^3-576x+6798\)	1006.2.0.?	$[(57, 371)]$
32192.h1	32192u1	32192.h	32192u	$1$	$1$	\( 2^{6} \cdot 503 \)	\( - 2^{28} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$4.569796145$	$1$		$8$	$23040$	$0.845325$	$-1349232625/515072$	$0.83497$	$3.27628$	$[0, -1, 0, -1473, -27551]$	\(y^2=x^3-x^2-1473x-27551\)	1006.2.0.?	$[(165, 2048), (1189, 40960)]$
32192.v1	32192h1	32192.v	32192h	$1$	$1$	\( 2^{6} \cdot 503 \)	\( - 2^{28} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$23040$	$0.845325$	$-1349232625/515072$	$0.83497$	$3.27628$	$[0, 1, 0, -1473, 27551]$	\(y^2=x^3+x^2-1473x+27551\)	1006.2.0.?	$[]$
49294.g1	49294e1	49294.g	49294e	$1$	$1$	\( 2 \cdot 7^{2} \cdot 503 \)	\( - 2^{10} \cdot 7^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$2.649589173$	$1$		$2$	$45360$	$0.778560$	$-1349232625/515072$	$0.83497$	$3.07294$	$[1, 0, 0, -1128, -18880]$	\(y^2+xy=x^3-1128x-18880\)	1006.2.0.?	$[(40, 0)]$
72432.s1	72432bp1	72432.s	72432bp	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 503 \)	\( - 2^{22} \cdot 3^{6} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$3.106989612$	$1$		$8$	$86400$	$1.048058$	$-1349232625/515072$	$0.83497$	$3.25626$	$[0, 0, 0, -3315, 94642]$	\(y^2=x^3-3315x+94642\)	1006.2.0.?	$[(9, 256), (337/3, 4096/3)]$
121726.c1	121726b1	121726.c	121726b	$1$	$1$	\( 2 \cdot 11^{2} \cdot 503 \)	\( - 2^{10} \cdot 11^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$142800$	$1.004553$	$-1349232625/515072$	$0.83497$	$3.06731$	$[1, 1, 0, -2785, -74059]$	\(y^2+xy=x^3+x^2-2785x-74059\)	1006.2.0.?	$[]$
170014.b1	170014g1	170014.b	170014g	$1$	$1$	\( 2 \cdot 13^{2} \cdot 503 \)	\( - 2^{10} \cdot 13^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$246240$	$1.088079$	$-1349232625/515072$	$0.83497$	$3.06545$	$[1, 1, 0, -3890, 118708]$	\(y^2+xy=x^3+x^2-3890x+118708\)	1006.2.0.?	$[]$
201200.n1	201200g1	201200.n	201200g	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 503 \)	\( - 2^{22} \cdot 5^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$4.189852135$	$1$		$2$	$414720$	$1.303471$	$-1349232625/515072$	$0.83497$	$3.23482$	$[0, -1, 0, -9208, -435088]$	\(y^2=x^3-x^2-9208x-435088\)	1006.2.0.?	$[(1436, 54272)]$
226350.bn1	226350k1	226350.bn	226350k	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 503 \)	\( - 2^{10} \cdot 3^{6} \cdot 5^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$518400$	$1.159630$	$-1349232625/515072$	$0.83497$	$3.06393$	$[1, -1, 1, -5180, -183553]$	\(y^2+xy+y=x^3-x^2-5180x-183553\)	1006.2.0.?	$[]$
289728.cm1	289728cm1	289728.cm	289728cm	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 503 \)	\( - 2^{28} \cdot 3^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$691200$	$1.394632$	$-1349232625/515072$	$0.83497$	$3.22801$	$[0, 0, 0, -13260, 757136]$	\(y^2=x^3-13260x+757136\)	1006.2.0.?	$[]$
289728.cu1	289728cu1	289728.cu	289728cu	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 503 \)	\( - 2^{28} \cdot 3^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$4$	$2$	$0$	$691200$	$1.394632$	$-1349232625/515072$	$0.83497$	$3.22801$	$[0, 0, 0, -13260, -757136]$	\(y^2=x^3-13260x-757136\)	1006.2.0.?	$[]$
290734.f1	290734f1	290734.f	290734f	$1$	$1$	\( 2 \cdot 17^{2} \cdot 503 \)	\( - 2^{10} \cdot 17^{6} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1.885309106$	$1$		$8$	$622080$	$1.222212$	$-1349232625/515072$	$0.83497$	$3.06265$	$[1, 0, 0, -6653, 268529]$	\(y^2+xy=x^3-6653x+268529\)	1006.2.0.?	$[(-10, 583), (1066/3, 27301/3)]$
363166.c1	363166c1	363166.c	363166c	$1$	$1$	\( 2 \cdot 19^{2} \cdot 503 \)	\( - 2^{10} \cdot 19^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$5.559282757$	$1$		$0$	$786240$	$1.277824$	$-1349232625/515072$	$0.83497$	$3.06157$	$[1, 0, 1, -8311, -376358]$	\(y^2+xy+y=x^3-8311x-376358\)	1006.2.0.?	$[(21167/11, 2383924/11)]$
394352.j1	394352j1	394352.j	394352j	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 503 \)	\( - 2^{22} \cdot 7^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$1088640$	$1.471706$	$-1349232625/515072$	$0.83497$	$3.22256$	$[0, -1, 0, -18048, 1208320]$	\(y^2=x^3-x^2-18048x+1208320\)	1006.2.0.?	$[]$
443646.r1	443646r1	443646.r	443646r	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 503 \)	\( - 2^{10} \cdot 3^{6} \cdot 7^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$1360800$	$1.327866$	$-1349232625/515072$	$0.83497$	$3.06062$	$[1, -1, 0, -10152, 509760]$	\(y^2+xy=x^3-x^2-10152x+509760\)	1006.2.0.?	$[]$