Elliptic curve search results

Results (28 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
7392.c2	7392k3	7392.c	7392k	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{2} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.53	2B	$88$	$48$	$0$	$1.254626574$	$1$		$9$	$10240$	$1.071024$	$1400416996672/570715299$	$1.03227$	$4.07330$	$[0, -1, 0, -3729, -46431]$	\(y^2=x^3-x^2-3729x-46431\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 44.24.0-44.h.1.2, 88.48.0.?	$[(81, 420)]$
7392.h2	7392e2	7392.h	7392e	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{2} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.63	2B	$88$	$48$	$0$	$2.944972789$	$1$		$3$	$10240$	$1.071024$	$1400416996672/570715299$	$1.03227$	$4.07330$	$[0, 1, 0, -3729, 46431]$	\(y^2=x^3+x^2-3729x+46431\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.3, 44.24.0-44.h.1.1, 88.48.0.?	$[(-3, 240)]$
14784.x4	14784c1	14784.x	14784c	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{6} \cdot 3^{2} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.102	2B	$88$	$48$	$0$	$4.330670544$	$1$		$3$	$10240$	$0.724449$	$1400416996672/570715299$	$1.03227$	$3.34608$	$[0, -1, 0, -932, 6270]$	\(y^2=x^3-x^2-932x+6270\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 44.12.0.h.1, 88.48.0.?	$[(67, 490)]$
14784.ck4	14784bl1	14784.ck	14784bl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{6} \cdot 3^{2} \cdot 7^{8} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.104	2B	$88$	$48$	$0$	$1$	$1$		$1$	$10240$	$0.724449$	$1400416996672/570715299$	$1.03227$	$3.34608$	$[0, 1, 0, -932, -6270]$	\(y^2=x^3+x^2-932x-6270\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.7, 44.12.0.h.1, 88.48.0.?	$[ ]$
22176.r2	22176k3	22176.r	22176k	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$264$	$48$	$0$	$3.922520402$	$1$		$3$	$81920$	$1.620329$	$1400416996672/570715299$	$1.03227$	$4.28482$	$[0, 0, 0, -33564, -1287200]$	\(y^2=x^3-33564x-1287200\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.1, 24.24.0-8.m.1.6, $\ldots$	$[(-42, 220)]$
22176.w2	22176i3	22176.w	22176i	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$264$	$48$	$0$	$1$	$1$		$1$	$81920$	$1.620329$	$1400416996672/570715299$	$1.03227$	$4.28482$	$[0, 0, 0, -33564, 1287200]$	\(y^2=x^3-33564x+1287200\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.8, $\ldots$	$[ ]$
44352.bf4	44352bp1	44352.bf	44352bp	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 \)	\( 2^{6} \cdot 3^{8} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$264$	$48$	$0$	$8.091624304$	$1$		$1$	$81920$	$1.273756$	$1400416996672/570715299$	$1.03227$	$3.61857$	$[0, 0, 0, -8391, -160900]$	\(y^2=x^3-8391x-160900\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.7, 44.12.0.h.1, $\ldots$	$[(2836/3, 144100/3)]$
44352.bm4	44352cd1	44352.bm	44352cd	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 \)	\( 2^{6} \cdot 3^{8} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$264$	$48$	$0$	$1.875591516$	$1$		$3$	$81920$	$1.273756$	$1400416996672/570715299$	$1.03227$	$3.61857$	$[0, 0, 0, -8391, 160900]$	\(y^2=x^3-8391x+160900\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.5, 44.12.0.h.1, $\ldots$	$[(96, 490)]$
51744.bb2	51744v3	51744.bb	51744v	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3^{2} \cdot 7^{14} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$616$	$48$	$0$	$6.439273096$	$1$		$1$	$491520$	$2.043980$	$1400416996672/570715299$	$1.03227$	$4.41872$	$[0, -1, 0, -182737, -16291295]$	\(y^2=x^3-x^2-182737x-16291295\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 28.12.0-4.c.1.1, 44.12.0.h.1, $\ldots$	$[(-5471/4, 158025/4)]$
51744.cg2	51744ci3	51744.cg	51744ci	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3^{2} \cdot 7^{14} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$616$	$48$	$0$	$1$	$1$		$1$	$491520$	$2.043980$	$1400416996672/570715299$	$1.03227$	$4.41872$	$[0, 1, 0, -182737, 16291295]$	\(y^2=x^3+x^2-182737x+16291295\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 28.12.0-4.c.1.2, 44.12.0.h.1, $\ldots$	$[ ]$
81312.d2	81312d3	81312.d	81312d	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7 \cdot 11^{2} \)	\( 2^{12} \cdot 3^{2} \cdot 7^{8} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.64	2B	$88$	$48$	$0$	$1$	$1$		$1$	$1228800$	$2.269970$	$1400416996672/570715299$	$1.03227$	$4.48193$	$[0, -1, 0, -451249, 63604609]$	\(y^2=x^3-x^2-451249x+63604609\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.6, 44.24.0-44.h.1.1, 88.48.0.?	$[ ]$
81312.bf2	81312bv3	81312.bf	81312bv	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7 \cdot 11^{2} \)	\( 2^{12} \cdot 3^{2} \cdot 7^{8} \cdot 11^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.54	2B	$88$	$48$	$0$	$2.300072476$	$1$		$7$	$1228800$	$2.269970$	$1400416996672/570715299$	$1.03227$	$4.48193$	$[0, 1, 0, -451249, -63604609]$	\(y^2=x^3+x^2-451249x-63604609\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.8, 44.24.0-44.h.1.2, 88.48.0.?	$[(-149, 588)]$
103488.bk4	103488ca1	103488.bk	103488ca	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{6} \cdot 3^{2} \cdot 7^{14} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$616$	$48$	$0$	$6.004700098$	$1$		$3$	$491520$	$1.697405$	$1400416996672/570715299$	$1.03227$	$3.79331$	$[0, -1, 0, -45684, 2059254]$	\(y^2=x^3-x^2-45684x+2059254\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 44.12.0.h.1, 56.24.0-8.m.1.2, $\ldots$	$[(343, 5160)]$
103488.fm4	103488dh1	103488.fm	103488dh	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 \)	\( 2^{6} \cdot 3^{2} \cdot 7^{14} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$616$	$48$	$0$	$10.28332650$	$1$		$1$	$491520$	$1.697405$	$1400416996672/570715299$	$1.03227$	$3.79331$	$[0, 1, 0, -45684, -2059254]$	\(y^2=x^3+x^2-45684x-2059254\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 44.12.0.h.1, 56.24.0-8.m.1.1, $\ldots$	$[(20317/9, 1111690/9)]$
155232.r2	155232q4	155232.r	155232q	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3^{8} \cdot 7^{14} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$3932160$	$2.593285$	$1400416996672/570715299$	$1.03227$	$4.56406$	$[0, 0, 0, -1644636, 441509600]$	\(y^2=x^3-1644636x+441509600\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 44.12.0.h.1, 84.12.0.?, $\ldots$	$[ ]$
155232.bi2	155232dd2	155232.bi	155232dd	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3^{8} \cdot 7^{14} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$3932160$	$2.593285$	$1400416996672/570715299$	$1.03227$	$4.56406$	$[0, 0, 0, -1644636, -441509600]$	\(y^2=x^3-1644636x-441509600\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 44.12.0.h.1, 84.12.0.?, $\ldots$	$[ ]$
162624.dm4	162624io1	162624.dm	162624io	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} \)	\( 2^{6} \cdot 3^{2} \cdot 7^{8} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.114	2B	$88$	$48$	$0$	$3.494315985$	$1$		$3$	$1228800$	$1.923397$	$1400416996672/570715299$	$1.03227$	$3.87643$	$[0, -1, 0, -112812, -7894170]$	\(y^2=x^3-x^2-112812x-7894170\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.2, 44.12.0.h.1, 88.48.0.?	$[(-81, 840)]$
162624.hw4	162624gf1	162624.hw	162624gf	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} \)	\( 2^{6} \cdot 3^{2} \cdot 7^{8} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.110	2B	$88$	$48$	$0$	$8.423303834$	$1$		$1$	$1228800$	$1.923397$	$1400416996672/570715299$	$1.03227$	$3.87643$	$[0, 1, 0, -112812, 7894170]$	\(y^2=x^3+x^2-112812x+7894170\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.4, 44.12.0.h.1, 88.48.0.?	$[(1641/5, 110136/5)]$
184800.cw2	184800cn4	184800.cw	184800cn	$4$	$4$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{6} \cdot 7^{8} \cdot 11 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$440$	$48$	$0$	$0.556981086$	$1$		$31$	$1310720$	$1.875742$	$1400416996672/570715299$	$1.03227$	$3.78841$	$[0, -1, 0, -93233, 5990337]$	\(y^2=x^3-x^2-93233x+5990337\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 20.12.0-4.c.1.1, 40.24.0-8.m.1.3, $\ldots$	$[(17, 2100), (-88, 3675)]$
184800.du2	184800fm2	184800.du	184800fm	$4$	$4$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{6} \cdot 7^{8} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$440$	$48$	$0$	$1$	$1$		$1$	$1310720$	$1.875742$	$1400416996672/570715299$	$1.03227$	$3.78841$	$[0, 1, 0, -93233, -5990337]$	\(y^2=x^3+x^2-93233x-5990337\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 20.12.0-4.c.1.2, 40.24.0-8.m.1.1, $\ldots$	$[ ]$
243936.cu2	243936cu2	243936.cu	243936cu	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$264$	$48$	$0$	$1$	$1$		$1$	$9830400$	$2.819275$	$1400416996672/570715299$	$1.03227$	$4.61638$	$[0, 0, 0, -4061244, -1713263200]$	\(y^2=x^3-4061244x-1713263200\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.1, 24.24.0-8.m.1.3, $\ldots$	$[ ]$
243936.dd2	243936dd4	243936.dd	243936dd	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$264$	$48$	$0$	$1$	$1$		$1$	$9830400$	$2.819275$	$1400416996672/570715299$	$1.03227$	$4.61638$	$[0, 0, 0, -4061244, 1713263200]$	\(y^2=x^3-4061244x+1713263200\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.1, $\ldots$	$[ ]$
310464.nr4	310464nr1	310464.nr	310464nr	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{6} \cdot 3^{8} \cdot 7^{14} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$1848$	$48$	$0$	$27.53526639$	$1$		$1$	$3932160$	$2.246712$	$1400416996672/570715299$	$1.03227$	$3.98502$	$[0, 0, 0, -411159, -55188700]$	\(y^2=x^3-411159x-55188700\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 44.12.0.h.1, 88.24.0.?, $\ldots$	$[(894334146400/6507, 845372731999618810/6507)]$
310464.pj4	310464pj1	310464.pj	310464pj	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{6} \cdot 3^{8} \cdot 7^{14} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$1848$	$48$	$0$	$1$	$4$	$2$	$1$	$3932160$	$2.246712$	$1400416996672/570715299$	$1.03227$	$3.98502$	$[0, 0, 0, -411159, 55188700]$	\(y^2=x^3-411159x+55188700\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 44.12.0.h.1, 88.24.0.?, $\ldots$	$[ ]$
369600.fd4	369600fd1	369600.fd	369600fd	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{6} \cdot 7^{8} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$440$	$48$	$0$	$1$	$1$		$1$	$1310720$	$1.529169$	$1400416996672/570715299$	$1.03227$	$3.25918$	$[0, -1, 0, -23308, -737138]$	\(y^2=x^3-x^2-23308x-737138\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 40.24.0-8.m.1.4, 44.12.0.h.1, $\ldots$	$[ ]$
369600.sx4	369600sx1	369600.sx	369600sx	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{6} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$440$	$48$	$0$	$1.499870176$	$1$		$3$	$1310720$	$1.529169$	$1400416996672/570715299$	$1.03227$	$3.25918$	$[0, 1, 0, -23308, 737138]$	\(y^2=x^3+x^2-23308x+737138\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 40.24.0-8.m.1.2, 44.12.0.h.1, $\ldots$	$[(29, 294)]$
487872.dv4	487872dv1	487872.dv	487872dv	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{6} \cdot 3^{8} \cdot 7^{8} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$264$	$48$	$0$	$23.17299002$	$1$		$1$	$9830400$	$2.472702$	$1400416996672/570715299$	$1.03227$	$4.05455$	$[0, 0, 0, -1015311, -214157900]$	\(y^2=x^3-1015311x-214157900\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.2, 44.12.0.h.1, $\ldots$	$[(92421068476/8211, 17241315245171380/8211)]$
487872.et4	487872et1	487872.et	487872et	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{6} \cdot 3^{8} \cdot 7^{8} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$264$	$48$	$0$	$1$	$1$		$1$	$9830400$	$2.472702$	$1400416996672/570715299$	$1.03227$	$4.05455$	$[0, 0, 0, -1015311, 214157900]$	\(y^2=x^3-1015311x+214157900\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.4, 44.12.0.h.1, $\ldots$	$[ ]$

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