Elliptic curve search results

Results (17 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
4830.ba2	4830ba3	4830.ba	4830ba	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{8} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.58	2B	$184$	$48$	$0$	$1.269633329$	$1$		$6$	$36864$	$1.657282$	$5186062692284555089/2903809817953800$	$1.00969$	$5.08010$	$[1, 0, 0, -36061, 471785]$	\(y^2+xy=x^3-36061x+471785\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 184.48.0.?	$[(-64, 1619)]$
14490.t2	14490v4	14490.t	14490v	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{3} \cdot 3^{8} \cdot 5^{2} \cdot 7^{8} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$552$	$48$	$0$	$1$	$1$		$0$	$294912$	$2.206589$	$5186062692284555089/2903809817953800$	$1.00969$	$5.18558$	$[1, -1, 0, -324549, -12738195]$	\(y^2+xy=x^3-x^2-324549x-12738195\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 12.12.0-4.c.1.1, 24.24.0-8.k.1.1, $\ldots$	$[]$
24150.p2	24150m3	24150.p	24150m	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{3} \cdot 3^{2} \cdot 5^{8} \cdot 7^{8} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$920$	$48$	$0$	$0.656795917$	$1$		$8$	$884736$	$2.462002$	$5186062692284555089/2903809817953800$	$1.00969$	$5.22681$	$[1, 1, 0, -901525, 58973125]$	\(y^2+xy=x^3+x^2-901525x+58973125\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 20.12.0-4.c.1.1, 40.24.0-8.k.1.1, $\ldots$	$[(25, 6025)]$
33810.cm2	33810ch3	33810.cm	33810ch	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{14} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1288$	$48$	$0$	$1$	$1$		$0$	$1769472$	$2.630238$	$5186062692284555089/2903809817953800$	$1.00969$	$5.25175$	$[1, 1, 1, -1766990, -163589245]$	\(y^2+xy+y=x^3+x^2-1766990x-163589245\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 28.12.0-4.c.1.1, 56.24.0-8.k.1.1, $\ldots$	$[]$
38640.v2	38640br3	38640.v	38640br	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{15} \cdot 3^{2} \cdot 5^{2} \cdot 7^{8} \cdot 23^{4} \)	$2$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.49	2B	$184$	$48$	$0$	$1.282089091$	$1$		$37$	$884736$	$2.350430$	$5186062692284555089/2903809817953800$	$1.00969$	$4.86746$	$[0, -1, 0, -576976, -30194240]$	\(y^2=x^3-x^2-576976x-30194240\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.k.1.2, 184.48.0.?	$[(-664, 7728), (808, 5520)]$
72450.em2	72450ec3	72450.em	72450ec	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{3} \cdot 3^{8} \cdot 5^{8} \cdot 7^{8} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$2760$	$48$	$0$	$1$	$1$		$0$	$7077888$	$3.011307$	$5186062692284555089/2903809817953800$	$1.00969$	$5.30271$	$[1, -1, 1, -8113730, -1600388103]$	\(y^2+xy+y=x^3-x^2-8113730x-1600388103\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 60.12.0-4.c.1.1, 120.24.0.?, $\ldots$	$[]$
101430.v2	101430bg3	101430.v	101430bg	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{3} \cdot 3^{8} \cdot 5^{2} \cdot 7^{14} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$3864$	$48$	$0$	$1$	$1$		$0$	$14155776$	$3.179543$	$5186062692284555089/2903809817953800$	$1.00969$	$5.32307$	$[1, -1, 0, -15902910, 4401006700]$	\(y^2+xy=x^3-x^2-15902910x+4401006700\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 84.12.0.?, 168.24.0.?, $\ldots$	$[]$
111090.dn2	111090dm3	111090.dn	111090dm	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{8} \cdot 23^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.105	2B	$184$	$48$	$0$	$1$	$1$		$0$	$19464192$	$3.225029$	$5186062692284555089/2903809817953800$	$1.00969$	$5.32837$	$[1, 0, 0, -19076280, -5778360648]$	\(y^2+xy=x^3-19076280x-5778360648\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.k.1.3, 92.12.0.?, 184.48.0.?	$[]$
115920.es2	115920es3	115920.es	115920es	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{15} \cdot 3^{8} \cdot 5^{2} \cdot 7^{8} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$552$	$48$	$0$	$2.358598189$	$1$		$7$	$7077888$	$2.899734$	$5186062692284555089/2903809817953800$	$1.00969$	$4.97416$	$[0, 0, 0, -5192787, 820437266]$	\(y^2=x^3-5192787x+820437266\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 12.12.0-4.c.1.2, 24.24.0-8.k.1.2, $\ldots$	$[(47, 24010)]$
154560.cq2	154560gy4	154560.cq	154560gy	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{21} \cdot 3^{2} \cdot 5^{2} \cdot 7^{8} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.58	2B	$184$	$48$	$0$	$1$	$1$		$1$	$7077888$	$2.697002$	$5186062692284555089/2903809817953800$	$1.00969$	$4.65079$	$[0, -1, 0, -2307905, 243861825]$	\(y^2=x^3-x^2-2307905x+243861825\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 184.48.0.?	$[]$
154560.hu2	154560c3	154560.hu	154560c	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{21} \cdot 3^{2} \cdot 5^{2} \cdot 7^{8} \cdot 23^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.49	2B	$184$	$48$	$0$	$1$	$1$		$3$	$7077888$	$2.697002$	$5186062692284555089/2903809817953800$	$1.00969$	$4.65079$	$[0, 1, 0, -2307905, -243861825]$	\(y^2=x^3+x^2-2307905x-243861825\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.k.1.2, 184.48.0.?	$[]$
169050.de2	169050ge3	169050.de	169050ge	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{3} \cdot 3^{2} \cdot 5^{8} \cdot 7^{14} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$6440$	$48$	$0$	$1$	$1$		$0$	$42467328$	$3.434956$	$5186062692284555089/2903809817953800$	$1.00969$	$5.35179$	$[1, 0, 1, -44174751, -20360306102]$	\(y^2+xy+y=x^3-44174751x-20360306102\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 140.12.0.?, 184.24.0.?, $\ldots$	$[]$
193200.eq2	193200cg3	193200.eq	193200cg	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{15} \cdot 3^{2} \cdot 5^{8} \cdot 7^{8} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$920$	$48$	$0$	$14.32981239$	$1$		$1$	$21233664$	$3.155148$	$5186062692284555089/2903809817953800$	$1.00969$	$5.01721$	$[0, 1, 0, -14424408, -3803128812]$	\(y^2=x^3+x^2-14424408x-3803128812\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 20.12.0-4.c.1.2, 40.24.0-8.k.1.2, $\ldots$	$[(271353708/83, 4449050373306/83)]$
270480.ip2	270480ip4	270480.ip	270480ip	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{15} \cdot 3^{2} \cdot 5^{2} \cdot 7^{14} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1288$	$48$	$0$	$1$	$1$		$1$	$42467328$	$3.323383$	$5186062692284555089/2903809817953800$	$1.00969$	$5.04365$	$[0, 1, 0, -28271840, 10413167988]$	\(y^2=x^3+x^2-28271840x+10413167988\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 28.12.0-4.c.1.2, 56.24.0-8.k.1.2, $\ldots$	$[]$
333270.bb2	333270bb4	333270.bb	333270bb	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{3} \cdot 3^{8} \cdot 5^{2} \cdot 7^{8} \cdot 23^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$552$	$48$	$0$	$1$	$1$		$0$	$155713536$	$3.774334$	$5186062692284555089/2903809817953800$	$1.00969$	$5.38639$	$[1, -1, 0, -171686520, 156015737496]$	\(y^2+xy=x^3-x^2-171686520x+156015737496\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 24.24.0-8.k.1.3, 184.24.0.?, $\ldots$	$[]$
463680.cb2	463680cb3	463680.cb	463680cb	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{21} \cdot 3^{8} \cdot 5^{2} \cdot 7^{8} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$552$	$48$	$0$	$6.691656036$	$1$		$1$	$56623104$	$3.246307$	$5186062692284555089/2903809817953800$	$1.00969$	$4.76440$	$[0, 0, 0, -20771148, -6563498128]$	\(y^2=x^3-20771148x-6563498128\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 12.12.0-4.c.1.1, 24.24.0-8.k.1.1, $\ldots$	$[(-3271/2, 794995/2)]$
463680.fu2	463680fu4	463680.fu	463680fu	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{21} \cdot 3^{8} \cdot 5^{2} \cdot 7^{8} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$552$	$48$	$0$	$1$	$1$		$1$	$56623104$	$3.246307$	$5186062692284555089/2903809817953800$	$1.00969$	$4.76440$	$[0, 0, 0, -20771148, 6563498128]$	\(y^2=x^3-20771148x+6563498128\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 12.12.0-4.c.1.2, 24.24.0-8.k.1.2, $\ldots$	$[]$