Elliptic curves over $\Q$ of conductor 31768

Results (13 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
31768.a1	31768i1	31768.a	31768i	$1$	$1$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( - 2^{11} \cdot 11 \cdot 19^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$88$	$2$	$0$	$2.492044274$	$1$		$2$	$23616$	$0.737370$	$-11281250/11$	$0.94128$	$3.43835$	$[0, 1, 0, -3008, 62560]$	\(y^2=x^3+x^2-3008x+62560\)	88.2.0.?	$[(31, 8)]$
31768.b1	31768g1	31768.b	31768g	$1$	$1$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( - 2^{8} \cdot 11 \cdot 19^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1.669569764$	$1$		$4$	$230400$	$1.921236$	$-101634915328/1433531$	$0.88831$	$4.68643$	$[0, -1, 0, -222857, 41058589]$	\(y^2=x^3-x^2-222857x+41058589\)	22.2.0.a.1	$[(279, 722)]$
31768.c1	31768j1	31768.c	31768j	$1$	$1$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( 2^{4} \cdot 11^{6} \cdot 19^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$836$	$12$	$0$	$0.452570617$	$1$		$12$	$15552$	$0.655360$	$16746513664/1771561$	$0.89149$	$3.10653$	$[0, -1, 0, -956, 10609]$	\(y^2=x^3-x^2-956x+10609\)	2.2.0.a.1, 38.6.0.a.1, 836.12.0.?	$[(-28, 121), (5, 77)]$
31768.d1	31768e1	31768.d	31768e	$1$	$1$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( - 2^{11} \cdot 11^{6} \cdot 19^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$152$	$2$	$0$	$15.35634838$	$1$		$0$	$518400$	$2.404255$	$-7559297810066/33659659$	$0.92634$	$5.30114$	$[0, -1, 0, -1874432, -990931028]$	\(y^2=x^3-x^2-1874432x-990931028\)	152.2.0.?	$[(154377237/142, 1884916691779/142)]$
31768.e1	31768f1	31768.e	31768f	$1$	$1$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( 2^{4} \cdot 11^{2} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$836$	$12$	$0$	$0.375625896$	$1$		$4$	$4032$	$-0.132094$	$1668352/121$	$0.72131$	$2.21767$	$[0, -1, 0, -44, 121]$	\(y^2=x^3-x^2-44x+121\)	2.2.0.a.1, 38.6.0.a.1, 836.12.0.?	$[(0, 11)]$
31768.f1	31768d4	31768.f	31768d	$4$	$4$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( 2^{11} \cdot 11^{4} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1672$	$48$	$0$	$12.80535381$	$1$		$1$	$207360$	$1.977987$	$33279932754/278179$	$1.00454$	$4.77701$	$[0, 0, 0, -307211, -65064474]$	\(y^2=x^3-307211x-65064474\)	2.3.0.a.1, 4.12.0-4.c.1.2, 88.24.0.?, 152.24.0.?, 1672.48.0.?	$[(-561263/42, 50891455/42)]$
31768.f2	31768d2	31768.f	31768d	$4$	$4$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( 2^{10} \cdot 11^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1672$	$48$	$0$	$6.402676906$	$1$		$3$	$103680$	$1.631413$	$81385668/43681$	$1.02099$	$4.13003$	$[0, 0, 0, -32851, 617310]$	\(y^2=x^3-32851x+617310\)	2.6.0.a.1, 4.12.0-2.a.1.1, 88.24.0.?, 152.24.0.?, 836.24.0.?, $\ldots$	$[(-29/3, 22960/3)]$
31768.f3	31768d1	31768.f	31768d	$4$	$4$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( 2^{8} \cdot 11 \cdot 19^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1672$	$48$	$0$	$3.201338453$	$1$		$5$	$51840$	$1.284840$	$154617552/209$	$0.79224$	$4.05821$	$[0, 0, 0, -25631, 1577570]$	\(y^2=x^3-25631x+1577570\)	2.3.0.a.1, 4.12.0-4.c.1.1, 88.24.0.?, 152.24.0.?, 418.6.0.?, $\ldots$	$[(77, 246)]$
31768.f4	31768d3	31768.f	31768d	$4$	$4$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( - 2^{11} \cdot 11 \cdot 19^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1672$	$48$	$0$	$12.80535381$	$1$		$1$	$207360$	$1.977987$	$2295461646/1433531$	$0.93560$	$4.51905$	$[0, 0, 0, 125989, 4842454]$	\(y^2=x^3+125989x+4842454\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 88.24.0.?, 152.24.0.?, $\ldots$	$[(320926/15, 187497674/15)]$
31768.g1	31768b1	31768.g	31768b	$1$	$1$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( 2^{4} \cdot 11^{6} \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$836$	$12$	$0$	$1$	$1$		$0$	$295488$	$2.127579$	$16746513664/1771561$	$0.89149$	$4.81078$	$[0, 1, 0, -345236, -70695967]$	\(y^2=x^3+x^2-345236x-70695967\)	2.2.0.a.1, 38.6.0.a.1, 44.4.0-2.a.1.1, 836.12.0.?	$[]$
31768.h1	31768a1	31768.h	31768a	$1$	$1$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( 2^{4} \cdot 11^{2} \cdot 19^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	2.2.0.1	2Cn	$836$	$12$	$0$	$4.031585162$	$1$		$2$	$76608$	$1.340124$	$1668352/121$	$0.72131$	$3.92192$	$[0, 1, 0, -16004, -734167]$	\(y^2=x^3+x^2-16004x-734167\)	2.2.0.a.1, 38.6.0.a.1, 44.4.0-2.a.1.1, 836.12.0.?	$[(-64, 179)]$
31768.i1	31768c1	31768.i	31768c	$1$	$1$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( - 2^{11} \cdot 11 \cdot 19^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$88$	$2$	$0$	$123.9748129$	$1$		$0$	$448704$	$2.209591$	$-11281250/11$	$0.94128$	$5.14260$	$[0, -1, 0, -1086008, -435614836]$	\(y^2=x^3-x^2-1086008x-435614836\)	88.2.0.?	$[(684621290737229173306846885655801115242708059858937065/4021543274465478110342933, 566288289029421794640342220126163366611511388779921540773070174112119383848345414/4021543274465478110342933)]$
31768.j1	31768h1	31768.j	31768h	$1$	$1$	\( 2^{3} \cdot 11 \cdot 19^{2} \)	\( - 2^{8} \cdot 11 \cdot 19^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$4.748873035$	$1$		$0$	$55296$	$0.843008$	$-27648/11$	$0.78666$	$3.27626$	$[0, 0, 0, -1444, -27436]$	\(y^2=x^3-1444x-27436\)	22.2.0.a.1	$[(4180/3, 269306/3)]$