Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (26 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
2760.h1	2760h3	2760.h	2760h	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 23 \)	\( 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.58	2B	$7.296895918$	$1$		$3$	$24576$	$2.098572$	$544328872410114151778/14166950625$	$[0, 1, 0, -2160176, -1222750176]$	\(y^2=x^3+x^2-2160176x-1222750176\)
5520.e1	5520a4	5520.e	5520a	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 23 \)	\( 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 23^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.49	2B	$1$	$1$		$3$	$49152$	$2.098572$	$544328872410114151778/14166950625$	$[0, -1, 0, -2160176, 1222750176]$	\(y^2=x^3-x^2-2160176x+1222750176\)
8280.r1	8280k4	8280.r	8280k	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{4} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1$	$1$		$1$	$196608$	$2.647877$	$544328872410114151778/14166950625$	$[0, 0, 0, -19441587, 32994813166]$	\(y^2=x^3-19441587x+32994813166\)
13800.h1	13800c3	13800.h	13800c	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{4} \cdot 5^{10} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1$	$9$	$3$	$1$	$589824$	$2.903290$	$544328872410114151778/14166950625$	$[0, -1, 0, -54004408, -152735763188]$	\(y^2=x^3-x^2-54004408x-152735763188\)
16560.bp1	16560q3	16560.bp	16560q	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{4} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$4.700967676$	$1$		$3$	$393216$	$2.647877$	$544328872410114151778/14166950625$	$[0, 0, 0, -19441587, -32994813166]$	\(y^2=x^3-19441587x-32994813166\)
22080.bd1	22080m4	22080.bd	22080m	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 23 \)	\( 2^{17} \cdot 3^{4} \cdot 5^{4} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.58	2B	$1$	$1$		$1$	$393216$	$2.445145$	$544328872410114151778/14166950625$	$[0, -1, 0, -8640705, -9773360703]$	\(y^2=x^3-x^2-8640705x-9773360703\)
22080.cs1	22080cz4	22080.cs	22080cz	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 23 \)	\( 2^{17} \cdot 3^{4} \cdot 5^{4} \cdot 23^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.49	2B	$1.264284528$	$1$		$11$	$393216$	$2.445145$	$544328872410114151778/14166950625$	$[0, 1, 0, -8640705, 9773360703]$	\(y^2=x^3+x^2-8640705x+9773360703\)
27600.cr1	27600s4	27600.cr	27600s	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{4} \cdot 5^{10} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1$	$1$		$1$	$1179648$	$2.903290$	$544328872410114151778/14166950625$	$[0, 1, 0, -54004408, 152735763188]$	\(y^2=x^3+x^2-54004408x+152735763188\)
41400.bf1	41400bi4	41400.bf	41400bi	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{10} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$22.58818656$	$1$		$1$	$4718592$	$3.452595$	$544328872410114151778/14166950625$	$[0, 0, 0, -486039675, 4124351645750]$	\(y^2=x^3-486039675x+4124351645750\)
63480.v1	63480t4	63480.v	63480t	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 23^{2} \)	\( 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 23^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.105	2B	$5.557376499$	$1$		$3$	$12976128$	$3.666317$	$544328872410114151778/14166950625$	$[0, 1, 0, -1142733280, 14868059525600]$	\(y^2=x^3+x^2-1142733280x+14868059525600\)
66240.br1	66240ee4	66240.br	66240ee	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 \)	\( 2^{17} \cdot 3^{10} \cdot 5^{4} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$32.06545704$	$1$		$1$	$3145728$	$2.994450$	$544328872410114151778/14166950625$	$[0, 0, 0, -77766348, -263958505328]$	\(y^2=x^3-77766348x-263958505328\)
66240.bs1	66240bq4	66240.bs	66240bq	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 \)	\( 2^{17} \cdot 3^{10} \cdot 5^{4} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$4.209205266$	$1$		$3$	$3145728$	$2.994450$	$544328872410114151778/14166950625$	$[0, 0, 0, -77766348, 263958505328]$	\(y^2=x^3-77766348x+263958505328\)
82800.dc1	82800bd4	82800.dc	82800bd	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{10} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$24.54828557$	$1$		$1$	$9437184$	$3.452595$	$544328872410114151778/14166950625$	$[0, 0, 0, -486039675, -4124351645750]$	\(y^2=x^3-486039675x-4124351645750\)
110400.cp1	110400fi4	110400.cp	110400fi	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 23 \)	\( 2^{17} \cdot 3^{4} \cdot 5^{10} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1$	$1$		$1$	$9437184$	$3.249863$	$544328872410114151778/14166950625$	$[0, -1, 0, -216017633, 1222102123137]$	\(y^2=x^3-x^2-216017633x+1222102123137\)
110400.hf1	110400dl4	110400.hf	110400dl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 23 \)	\( 2^{17} \cdot 3^{4} \cdot 5^{10} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$13.78984390$	$1$		$1$	$9437184$	$3.249863$	$544328872410114151778/14166950625$	$[0, 1, 0, -216017633, -1222102123137]$	\(y^2=x^3+x^2-216017633x-1222102123137\)
126960.bj1	126960g4	126960.bj	126960g	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 23^{2} \)	\( 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 23^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.105	2B	$16.54883123$	$1$		$1$	$25952256$	$3.666317$	$544328872410114151778/14166950625$	$[0, -1, 0, -1142733280, -14868059525600]$	\(y^2=x^3-x^2-1142733280x-14868059525600\)
135240.bh1	135240bf3	135240.bh	135240bf	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 7^{6} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1$	$1$		$1$	$9437184$	$3.071526$	$544328872410114151778/14166950625$	$[0, -1, 0, -105848640, 419191613100]$	\(y^2=x^3-x^2-105848640x+419191613100\)
190440.m1	190440bj4	190440.m	190440bj	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 23^{2} \)	\( 2^{11} \cdot 3^{10} \cdot 5^{4} \cdot 23^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$91.08077928$	$1$		$1$	$103809024$	$4.215622$	$544328872410114151778/14166950625$	$[0, 0, 0, -10284599523, -401447891790722]$	\(y^2=x^3-10284599523x-401447891790722\)
270480.iq1	270480iq4	270480.iq	270480iq	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 7^{6} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$2.082538403$	$1$		$7$	$18874368$	$3.071526$	$544328872410114151778/14166950625$	$[0, 1, 0, -105848640, -419191613100]$	\(y^2=x^3+x^2-105848640x-419191613100\)
317400.q1	317400q3	317400.q	317400q	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 23^{2} \)	\( 2^{11} \cdot 3^{4} \cdot 5^{10} \cdot 23^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1$	$1$		$1$	$311427072$	$4.471039$	$544328872410114151778/14166950625$	$[0, -1, 0, -28568332008, 1858564577364012]$	\(y^2=x^3-x^2-28568332008x+1858564577364012\)
331200.ik1	331200ik3	331200.ik	331200ik	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 \)	\( 2^{17} \cdot 3^{10} \cdot 5^{10} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1$	$1$		$1$	$75497472$	$3.799171$	$544328872410114151778/14166950625$	$[0, 0, 0, -1944158700, 32994813166000]$	\(y^2=x^3-1944158700x+32994813166000\)
331200.il1	331200il4	331200.il	331200il	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 \)	\( 2^{17} \cdot 3^{10} \cdot 5^{10} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1$	$4$	$2$	$1$	$75497472$	$3.799171$	$544328872410114151778/14166950625$	$[0, 0, 0, -1944158700, -32994813166000]$	\(y^2=x^3-1944158700x-32994813166000\)
333960.co1	333960co3	333960.co	333960co	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 11^{6} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$8.222067857$	$1$		$3$	$35389440$	$3.297520$	$544328872410114151778/14166950625$	$[0, 1, 0, -261381336, 1626434958960]$	\(y^2=x^3+x^2-261381336x+1626434958960\)
380880.bp1	380880bp3	380880.bp	380880bp	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 23^{2} \)	\( 2^{11} \cdot 3^{10} \cdot 5^{4} \cdot 23^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$5.532055944$	$1$		$3$	$207618048$	$4.215622$	$544328872410114151778/14166950625$	$[0, 0, 0, -10284599523, 401447891790722]$	\(y^2=x^3-10284599523x+401447891790722\)
405720.bv1	405720bv4	405720.bv	405720bv	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{4} \cdot 7^{6} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$1$	$1$		$1$	$75497472$	$3.620834$	$544328872410114151778/14166950625$	$[0, 0, 0, -952637763, -11317220915938]$	\(y^2=x^3-952637763x-11317220915938\)
466440.cg1	466440cg4	466440.cg	466440cg	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 13^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 13^{6} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$5.409626110$	$4$	$2$	$3$	$56623104$	$3.381046$	$544328872410114151778/14166950625$	$[0, 1, 0, -365069800, -2684921857552]$	\(y^2=x^3+x^2-365069800x-2684921857552\)