Elliptic curve search results

Results (16 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
12342.n1	12342g2	12342.n	12342g	$2$	$2$	\( 2 \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{6} \cdot 11^{3} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$		$0$	$290304$	$2.421787$	$362515826352179162139875/203046912$	$1.06305$	$6.52187$	$[1, 0, 1, -16340316, 25422339226]$	\(y^2+xy+y=x^3-16340316x+25422339226\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$
12342.bc1	12342z2	12342.bc	12342z	$2$	$2$	\( 2 \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{6} \cdot 11^{9} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$4$	$2$	$0$	$3193344$	$3.620731$	$362515826352179162139875/203046912$	$1.06305$	$8.04907$	$[1, 0, 0, -1977178178, -33839110688316]$	\(y^2+xy=x^3-1977178178x-33839110688316\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$
37026.j1	37026d2	37026.j	37026d	$2$	$2$	\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{12} \cdot 11^{9} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$		$0$	$25546752$	$4.170036$	$362515826352179162139875/203046912$	$1.06305$	$7.83507$	$[1, -1, 0, -17794603602, 913655988584532]$	\(y^2+xy=x^3-x^2-17794603602x+913655988584532\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$
37026.bi1	37026w2	37026.bi	37026w	$2$	$2$	\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{12} \cdot 11^{3} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$4$	$2$	$0$	$2322432$	$2.971092$	$362515826352179162139875/203046912$	$1.06305$	$6.46737$	$[1, -1, 1, -147062840, -686403159109]$	\(y^2+xy+y=x^3-x^2-147062840x-686403159109\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$
98736.bb1	98736bm2	98736.bb	98736bm	$2$	$2$	\( 2^{4} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{6} \cdot 11^{3} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$4$	$2$	$1$	$6967296$	$3.114933$	$362515826352179162139875/203046912$	$1.06305$	$6.06588$	$[0, -1, 0, -261445048, -1627029710480]$	\(y^2=x^3-x^2-261445048x-1627029710480\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$
98736.bh1	98736bo2	98736.bh	98736bo	$2$	$2$	\( 2^{4} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{6} \cdot 11^{9} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$41.03238014$	$1$		$1$	$76640256$	$4.313881$	$362515826352179162139875/203046912$	$1.06305$	$7.31693$	$[0, -1, 0, -31634850848, 2165703084052224]$	\(y^2=x^3-x^2-31634850848x+2165703084052224\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[(47443552258574008434/21441185, 2798240450735357763848589102/21441185)]$
209814.k1	209814cs2	209814.k	209814cs	$2$	$2$	\( 2 \cdot 3 \cdot 11^{2} \cdot 17^{2} \)	\( 2^{14} \cdot 3^{6} \cdot 11^{3} \cdot 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$3.886633811$	$1$		$2$	$83607552$	$3.838390$	$362515826352179162139875/203046912$	$1.06305$	$6.40121$	$[1, 1, 0, -4722351185, 124904674969749]$	\(y^2+xy=x^3+x^2-4722351185x+124904674969749\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[(-56830, 14510783)]$
209814.ce1	209814bb2	209814.ce	209814bb	$2$	$2$	\( 2 \cdot 3 \cdot 11^{2} \cdot 17^{2} \)	\( 2^{14} \cdot 3^{6} \cdot 11^{9} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$4$	$2$	$0$	$919683072$	$5.037338$	$362515826352179162139875/203046912$	$1.06305$	$7.57531$	$[1, 1, 1, -571404493448, -166250979407203063]$	\(y^2+xy+y=x^3+x^2-571404493448x-166250979407203063\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$
296208.cy1	296208cy2	296208.cy	296208cy	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{12} \cdot 11^{3} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$4$	$2$	$1$	$55738368$	$3.664238$	$362515826352179162139875/203046912$	$1.06305$	$6.06013$	$[0, 0, 0, -2353005435, 43932155188394]$	\(y^2=x^3-2353005435x+43932155188394\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$
296208.dj1	296208dj2	296208.dj	296208dj	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{12} \cdot 11^{9} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$76.01227423$	$4$	$2$	$1$	$613122048$	$4.863190$	$362515826352179162139875/203046912$	$1.06305$	$7.20209$	$[0, 0, 0, -284713657635, -58473698555752414]$	\(y^2=x^3-284713657635x-58473698555752414\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[(29664952854942655298397068246178655/87601823946227, 5057826915064299216722248343056207895515025214190602/87601823946227)]$
308550.cg1	308550cg2	308550.cg	308550cg	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{6} \cdot 5^{6} \cdot 11^{9} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$142.2740325$	$1$		$0$	$459841536$	$4.425453$	$362515826352179162139875/203046912$	$1.06305$	$6.76325$	$[1, 1, 0, -49429454450, -4229888836039500]$	\(y^2+xy=x^3+x^2-49429454450x-4229888836039500\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[(-33310427776900389324808223832578288587685326195116300352387608489/509416692331967237211856841318, 8480247337274079750419443020113670479307538670030818016258811188943483511699212331474080114057/509416692331967237211856841318)]$
308550.fr1	308550fr2	308550.fr	308550fr	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{6} \cdot 5^{6} \cdot 11^{3} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1.380685301$	$1$		$4$	$41803776$	$3.226505$	$362515826352179162139875/203046912$	$1.06305$	$5.62498$	$[1, 1, 1, -408507888, 3177792403281]$	\(y^2+xy+y=x^3+x^2-408507888x+3177792403281\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[(11669, -5883)]$
394944.ce1	394944ce2	394944.ce	394944ce	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{32} \cdot 3^{6} \cdot 11^{9} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$100$	$2, 5$	$1$	$613122048$	$4.660454$	$362515826352179162139875/203046912$	$1.06305$	$6.85253$	$[0, -1, 0, -126539403393, -17325498133014399]$	\(y^2=x^3-x^2-126539403393x-17325498133014399\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$
394944.cp1	394944cp2	394944.cp	394944cp	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{32} \cdot 3^{6} \cdot 11^{3} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$22.60380367$	$1$		$1$	$55738368$	$3.461506$	$362515826352179162139875/203046912$	$1.06305$	$5.73606$	$[0, -1, 0, -1045780193, 13017283464033]$	\(y^2=x^3-x^2-1045780193x+13017283464033\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[(304494634783/4017, 3061115874462088/4017)]$
394944.gw1	394944gw2	394944.gw	394944gw	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{32} \cdot 3^{6} \cdot 11^{3} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$19.86009962$	$1$		$1$	$55738368$	$3.461506$	$362515826352179162139875/203046912$	$1.06305$	$5.73606$	$[0, 1, 0, -1045780193, -13017283464033]$	\(y^2=x^3+x^2-1045780193x-13017283464033\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[(3085884889/148, 166436102530203/148)]$
394944.hp1	394944hp2	394944.hp	394944hp	$2$	$2$	\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \)	\( 2^{32} \cdot 3^{6} \cdot 11^{9} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$4$	$2$	$1$	$613122048$	$4.660454$	$362515826352179162139875/203046912$	$1.06305$	$6.85253$	$[0, 1, 0, -126539403393, 17325498133014399]$	\(y^2=x^3+x^2-126539403393x+17325498133014399\)	2.3.0.a.1, 132.6.0.?, 204.6.0.?, 748.6.0.?, 2244.12.0.?	$[ ]$

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