Elliptic curves over $\Q$ of conductor 159953

Results (5 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
159953.a1	159953a4	159953.a	159953a	$4$	$4$	\( 17 \cdot 97^{2} \)	\( 17 \cdot 97^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.12	2B	$105536$	$1536$	$53$	$44.94309400$	$1$		$0$	$921600$	$1.910719$	$82483294977/17$	$1.03131$	$4.38836$	$[1, -1, 1, -853279, -303164890]$	\(y^2+xy+y=x^3-x^2-853279x-303164890\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0.j.1, 32.48.0.f.2, $\ldots$	$[(-725559568461953995941/1166598370, 433447054203642337600961283637/1166598370)]$
159953.a2	159953a2	159953.a	159953a	$4$	$4$	\( 17 \cdot 97^{2} \)	\( 17^{2} \cdot 97^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.20	2Cs	$52768$	$1536$	$53$	$22.47154700$	$1$		$2$	$460800$	$1.564146$	$20346417/289$	$1.02963$	$3.69507$	$[1, -1, 1, -53514, -4692592]$	\(y^2+xy+y=x^3-x^2-53514x-4692592\)	2.6.0.a.1, 4.12.0.a.1, 8.24.0.f.1, 16.48.0.c.2, 68.24.0.b.1, $\ldots$	$[(-7275034129/7685, 89939521027476/7685)]$
159953.a3	159953a3	159953.a	159953a	$4$	$4$	\( 17 \cdot 97^{2} \)	\( - 17^{4} \cdot 97^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.76	2B	$105536$	$1536$	$53$	$11.23577350$	$1$		$0$	$921600$	$1.910719$	$-35937/83521$	$1.18071$	$3.85859$	$[1, -1, 1, -6469, -12690242]$	\(y^2+xy+y=x^3-x^2-6469x-12690242\)	2.3.0.a.1, 4.12.0.d.1, 8.24.0.t.1, 16.48.0.m.2, 136.48.1.?, $\ldots$	$[(4409029/132, 2817105197/132)]$
159953.a4	159953a1	159953.a	159953a	$4$	$4$	\( 17 \cdot 97^{2} \)	\( 17 \cdot 97^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.12	2B	$105536$	$1536$	$53$	$11.23577350$	$1$		$1$	$230400$	$1.217571$	$35937/17$	$1.02432$	$3.16606$	$[1, -1, 1, -6469, 87180]$	\(y^2+xy+y=x^3-x^2-6469x+87180\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0.j.1, 32.48.0.f.2, $\ldots$	$[(-8832/29, 9682767/29)]$
159953.b1	159953b1	159953.b	159953b	$1$	$1$	\( 17 \cdot 97^{2} \)	\( - 17 \cdot 97^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6596$	$2$	$0$	$7.038796670$	$1$		$2$	$564480$	$1.585266$	$103823/1649$	$0.72633$	$3.52792$	$[1, 0, 0, 9213, 1751114]$	\(y^2+xy=x^3+9213x+1751114\)	6596.2.0.?	$[(1057, 34007)]$