Elliptic curve search results

Results (21 matches)

  Download displayed columns for results to

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
3990.g3	3990g2	3990.g	3990g	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{14} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$2280$	$48$	$0$	$1$	$1$		$2$	$53760$	$2.022373$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.31126$	$[1, 1, 0, -784007, -267513099]$	\(y^2+xy=x^3+x^2-784007x-267513099\)	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 76.12.0.?, 120.24.0.?, $\ldots$	$[ ]$
11970.bj3	11970br2	11970.bj	11970br	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{14} \cdot 3^{8} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$2280$	$48$	$0$	$0.941550080$	$1$		$14$	$430080$	$2.571678$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.27485$	$[1, -1, 1, -7056068, 7215797607]$	\(y^2+xy+y=x^3-x^2-7056068x+7215797607\)	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0-2.a.1.1, 120.24.0.?, 228.12.0.?, $\ldots$	$[(933, 37533)]$
19950.cy3	19950cw2	19950.cy	19950cw	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{14} \cdot 3^{2} \cdot 5^{12} \cdot 7^{4} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2280$	$48$	$0$	$1$	$1$		$2$	$1290240$	$2.827091$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.26067$	$[1, 0, 0, -19600188, -33399937008]$	\(y^2+xy=x^3-19600188x-33399937008\)	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 380.24.0.?, 456.24.0.?, $\ldots$	$[ ]$
27930.ba3	27930bi2	27930.ba	27930bi	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{14} \cdot 3^{2} \cdot 5^{6} \cdot 7^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15960$	$48$	$0$	$1$	$1$		$2$	$2580480$	$2.995327$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.25210$	$[1, 0, 1, -38416369, 91641743876]$	\(y^2+xy+y=x^3-38416369x+91641743876\)	2.6.0.a.1, 120.12.0.?, 140.12.0.?, 168.12.0.?, 380.12.0.?, $\ldots$	$[ ]$
31920.cc3	31920cb2	31920.cc	31920cb	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{26} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2280$	$48$	$0$	$1$	$1$		$3$	$1290240$	$2.715519$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.84784$	$[0, 1, 0, -12544120, 17095750100]$	\(y^2=x^3+x^2-12544120x+17095750100\)	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 76.12.0.?, 120.24.0.?, $\ldots$	$[ ]$
59850.di3	59850cd2	59850.di	59850cd	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{14} \cdot 3^{8} \cdot 5^{12} \cdot 7^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2280$	$48$	$0$	$2.809321282$	$1$		$8$	$10321920$	$3.376400$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.23463$	$[1, -1, 0, -176401692, 901798299216]$	\(y^2+xy=x^3-x^2-176401692x+901798299216\)	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 152.12.0.?, $\ldots$	$[(7533, 15984)]$
75810.dj3	75810do2	75810.dj	75810do	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19^{2} \)	\( 2^{14} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2280$	$48$	$0$	$1.467937852$	$1$		$8$	$19353600$	$3.494595$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.22969$	$[1, 0, 0, -283026715, 1832608132817]$	\(y^2+xy=x^3-283026715x+1832608132817\)	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 380.24.0.?, 456.24.0.?, $\ldots$	$[(9974, 39113)]$
83790.fq3	83790fr2	83790.fq	83790fr	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{14} \cdot 3^{8} \cdot 5^{6} \cdot 7^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15960$	$48$	$0$	$1$	$1$		$2$	$20643840$	$3.544636$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.22767$	$[1, -1, 1, -345747317, -2474327084659]$	\(y^2+xy+y=x^3-x^2-345747317x-2474327084659\)	2.6.0.a.1, 56.12.0-2.a.1.1, 120.12.0.?, 380.12.0.?, 420.12.0.?, $\ldots$	$[ ]$
95760.bl3	95760eb2	95760.bl	95760eb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{26} \cdot 3^{8} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$2280$	$48$	$0$	$6.788144011$	$1$		$5$	$10321920$	$3.264828$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.86242$	$[0, 0, 0, -112897083, -461698149782]$	\(y^2=x^3-112897083x-461698149782\)	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0-2.a.1.1, 120.24.0.?, 228.12.0.?, $\ldots$	$[(437519, 289311750)]$
127680.y3	127680dv2	127680.y	127680dv	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{32} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2280$	$48$	$0$	$4.221595556$	$1$		$5$	$10321920$	$3.062096$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.51205$	$[0, -1, 0, -50176481, 136816177281]$	\(y^2=x^3-x^2-50176481x+136816177281\)	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 152.12.0.?, $\ldots$	$[(3959, 14280)]$
127680.ed3	127680cg2	127680.ed	127680cg	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{32} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2280$	$48$	$0$	$37.42539067$	$1$		$3$	$10321920$	$3.062096$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.51205$	$[0, 1, 0, -50176481, -136816177281]$	\(y^2=x^3+x^2-50176481x-136816177281\)	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 152.12.0.?, $\ldots$	$[(345288479055938305/4679237, 177277752008494640478233496/4679237)]$
139650.ev3	139650dv2	139650.ev	139650dv	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{14} \cdot 3^{2} \cdot 5^{12} \cdot 7^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15960$	$48$	$0$	$1$	$1$		$2$	$61931520$	$3.800049$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.21785$	$[1, 1, 1, -960409213, 11455217984531]$	\(y^2+xy+y=x^3+x^2-960409213x+11455217984531\)	2.6.0.a.1, 28.12.0-2.a.1.1, 120.12.0.?, 380.12.0.?, 456.12.0.?, $\ldots$	$[ ]$
159600.bn3	159600ex2	159600.bn	159600ex	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{26} \cdot 3^{2} \cdot 5^{12} \cdot 7^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2280$	$48$	$0$	$7.079878497$	$1$		$3$	$30965760$	$3.520241$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.86828$	$[0, -1, 0, -313603008, 2137595968512]$	\(y^2=x^3-x^2-313603008x+2137595968512\)	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 380.24.0.?, 456.24.0.?, $\ldots$	$[(29213/2, 3892625/2)]$
223440.bt3	223440fg2	223440.bt	223440fg	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{26} \cdot 3^{2} \cdot 5^{6} \cdot 7^{10} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15960$	$48$	$0$	$21.78126001$	$1$		$3$	$61931520$	$3.688477$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.87188$	$[0, -1, 0, -614661896, -5865071608080]$	\(y^2=x^3-x^2-614661896x-5865071608080\)	2.6.0.a.1, 120.12.0.?, 140.12.0.?, 168.12.0.?, 380.12.0.?, $\ldots$	$[(1612301161673/2504, 2037346076913070875/2504)]$
227430.p3	227430fi2	227430.p	227430fi	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19^{2} \)	\( 2^{14} \cdot 3^{8} \cdot 5^{6} \cdot 7^{4} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2280$	$48$	$0$	$31.20059780$	$1$		$2$	$154828800$	$4.043900$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.20924$	$[1, -1, 0, -2547240435, -49480419586059]$	\(y^2+xy=x^3-x^2-2547240435x-49480419586059\)	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.2, 120.24.0.?, 152.12.0.?, $\ldots$	$[(19942082464326937/148129, 2810233136286358730388030/148129)]$
379050.bg3	379050bg2	379050.bg	379050bg	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{14} \cdot 3^{2} \cdot 5^{12} \cdot 7^{4} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2280$	$48$	$0$	$4.709939701$	$1$		$6$	$464486400$	$4.299309$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.20092$	$[1, 1, 0, -7075667875, 229076016602125]$	\(y^2+xy=x^3+x^2-7075667875x+229076016602125\)	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.2, 76.12.0.?, 120.24.0.?, $\ldots$	$[(-8685, 17030005)]$
383040.hx3	383040hx2	383040.hx	383040hx	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{32} \cdot 3^{8} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2280$	$48$	$0$	$1$	$1$		$3$	$82575360$	$3.611401$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.55375$	$[0, 0, 0, -451588332, 3693585198256]$	\(y^2=x^3-451588332x+3693585198256\)	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 380.24.0.?, 456.24.0.?, $\ldots$	$[ ]$
383040.on3	383040on2	383040.on	383040on	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{32} \cdot 3^{8} \cdot 5^{6} \cdot 7^{4} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2280$	$48$	$0$	$6.021274642$	$1$		$5$	$82575360$	$3.611401$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.55375$	$[0, 0, 0, -451588332, -3693585198256]$	\(y^2=x^3-451588332x-3693585198256\)	2.6.0.a.1, 4.12.0-2.a.1.1, 120.24.0.?, 380.24.0.?, 456.24.0.?, $\ldots$	$[(-48863/2, 31185/2)]$
418950.hx3	418950hx2	418950.hx	418950hx	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{14} \cdot 3^{8} \cdot 5^{12} \cdot 7^{10} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15960$	$48$	$0$	$1$	$9$	$3$	$2$	$495452160$	$4.349350$	$53294746224000958661881/1997017344000000$	$1.00829$	$6.19936$	$[1, -1, 0, -8643682917, -309299529265259]$	\(y^2+xy=x^3-x^2-8643682917x-309299529265259\)	2.6.0.a.1, 84.12.0.?, 120.12.0.?, 280.12.0.?, 380.12.0.?, $\ldots$	$[ ]$
478800.bb3	478800bb2	478800.bb	478800bb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{26} \cdot 3^{8} \cdot 5^{12} \cdot 7^{4} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2280$	$48$	$0$	$1$	$4$	$2$	$3$	$247726080$	$4.069550$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.87935$	$[0, 0, 0, -2822427075, -57712268722750]$	\(y^2=x^3-2822427075x-57712268722750\)	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 152.12.0.?, $\ldots$	$[ ]$
482790.fw3	482790fw2	482790.fw	482790fw	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( 2^{14} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 11^{6} \cdot 19^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$25080$	$48$	$0$	$0.533964066$	$1$		$58$	$68812800$	$3.221321$	$53294746224000958661881/1997017344000000$	$1.00829$	$5.09787$	$[1, 1, 1, -94864910, 355585610315]$	\(y^2+xy+y=x^3+x^2-94864910x+355585610315\)	2.6.0.a.1, 120.12.0.?, 220.12.0.?, 264.12.0.?, 380.12.0.?, $\ldots$	$[(5693, 5623), (4923, 86473)]$

  Download displayed columns for results to