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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
19110.cg1	19110bw1	19110.cg	19110bw	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.380959798$	$1$		$8$	$1693440$	$2.880959$	$-107920681386000721/1328441886720000$	$1.01988$	$5.87248$	$[1, 1, 1, -1778505, -4308958473]$	\(y^2+xy+y=x^3+x^2-1778505x-4308958473\)	52.2.0.a.1	$[(4087, 236096)]$
19110.cs1	19110cs1	19110.cs	19110cs	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{4} \cdot 7^{2} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.035207602$	$1$		$20$	$241920$	$1.908005$	$-107920681386000721/1328441886720000$	$1.01988$	$4.68811$	$[1, 0, 0, -36296, 12557376]$	\(y^2+xy=x^3-36296x+12557376\)	52.2.0.a.1	$[(-104, 3952)]$
57330.n1	57330n1	57330.n	57330n	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{14} \cdot 3^{16} \cdot 5^{4} \cdot 7^{8} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$13547520$	$3.430267$	$-107920681386000721/1328441886720000$	$1.01988$	$5.88527$	$[1, -1, 0, -16006545, 116325872221]$	\(y^2+xy=x^3-x^2-16006545x+116325872221\)	52.2.0.a.1	$[ ]$
57330.cd1	57330cq1	57330.cd	57330cq	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{14} \cdot 3^{16} \cdot 5^{4} \cdot 7^{2} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1.325570017$	$1$		$2$	$1935360$	$2.457310$	$-107920681386000721/1328441886720000$	$1.01988$	$4.81966$	$[1, -1, 0, -326664, -339049152]$	\(y^2+xy=x^3-x^2-326664x-339049152\)	52.2.0.a.1	$[(1872, 73944)]$
95550.by1	95550m1	95550.by	95550m	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{10} \cdot 7^{2} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$5806080$	$2.712723$	$-107920681386000721/1328441886720000$	$1.01988$	$4.87224$	$[1, 1, 0, -907400, 1569672000]$	\(y^2+xy=x^3+x^2-907400x+1569672000\)	52.2.0.a.1	$[ ]$
95550.ex1	95550dg1	95550.ex	95550dg	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{10} \cdot 7^{8} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1.994090473$	$1$		$4$	$40642560$	$3.685680$	$-107920681386000721/1328441886720000$	$1.01988$	$5.89038$	$[1, 0, 1, -44462626, -538530883852]$	\(y^2+xy+y=x^3-44462626x-538530883852\)	52.2.0.a.1	$[(30157, 5039321)]$
152880.ba1	152880eh1	152880.ba	152880eh	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{26} \cdot 3^{10} \cdot 5^{4} \cdot 7^{2} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$5806080$	$2.601151$	$-107920681386000721/1328441886720000$	$1.01988$	$4.56825$	$[0, -1, 0, -580736, -803672064]$	\(y^2=x^3-x^2-580736x-803672064\)	52.2.0.a.1	$[ ]$
152880.gw1	152880bo1	152880.gw	152880bo	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{26} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$40642560$	$3.574108$	$-107920681386000721/1328441886720000$	$1.01988$	$5.54630$	$[0, 1, 0, -28456080, 275716430100]$	\(y^2=x^3+x^2-28456080x+275716430100\)	52.2.0.a.1	$[ ]$
248430.o1	248430o1	248430.o	248430o	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 13^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$13.79697583$	$1$		$0$	$284497920$	$4.163437$	$-107920681386000721/1328441886720000$	$1.01988$	$5.89881$	$[1, 1, 0, -300567348, -9465278928048]$	\(y^2+xy=x^3+x^2-300567348x-9465278928048\)	52.2.0.a.1	$[(841659336/41, 24384899684412/41)]$
248430.ek1	248430ek1	248430.ek	248430ek	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{4} \cdot 7^{2} \cdot 13^{9} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.514600098$	$1$		$18$	$40642560$	$3.190479$	$-107920681386000721/1328441886720000$	$1.01988$	$4.95898$	$[1, 0, 1, -6134028, 27594689098]$	\(y^2+xy+y=x^3-6134028x+27594689098\)	52.2.0.a.1	$[(1184, 147705), (100049, 31586775)]$
286650.lr1	286650lr1	286650.lr	286650lr	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{14} \cdot 3^{16} \cdot 5^{10} \cdot 7^{2} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$46448640$	$3.262028$	$-107920681386000721/1328441886720000$	$1.01988$	$4.97083$	$[1, -1, 1, -8166605, -42389310603]$	\(y^2+xy+y=x^3-x^2-8166605x-42389310603\)	52.2.0.a.1	$[ ]$
286650.md1	286650md1	286650.md	286650md	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{14} \cdot 3^{16} \cdot 5^{10} \cdot 7^{8} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$325140480$	$4.234985$	$-107920681386000721/1328441886720000$	$1.01988$	$5.89996$	$[1, -1, 1, -400163630, 14540333863997]$	\(y^2+xy+y=x^3-x^2-400163630x+14540333863997\)	52.2.0.a.1	$[ ]$
458640.ej1	458640ej1	458640.ej	458640ej	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{26} \cdot 3^{16} \cdot 5^{4} \cdot 7^{8} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$53.36196982$	$1$		$0$	$325140480$	$4.123413$	$-107920681386000721/1328441886720000$	$1.01988$	$5.58454$	$[0, 0, 0, -256104723, -7444599717422]$	\(y^2=x^3-256104723x-7444599717422\)	52.2.0.a.1	$[(3084849088292598967985639/9991208821, 3752094559177420262686770883689981150/9991208821)]$
458640.mc1	458640mc1	458640.mc	458640mc	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{26} \cdot 3^{16} \cdot 5^{4} \cdot 7^{2} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$46448640$	$3.150459$	$-107920681386000721/1328441886720000$	$1.01988$	$4.68891$	$[0, 0, 0, -5226627, 21704372354]$	\(y^2=x^3-5226627x+21704372354\)	52.2.0.a.1	$[ ]$

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